THE INFLUENCE OF GEOMETRIC PARAMETERS ON STRENGTH PROPERTIES OF THE AGGREGATES USED TO PRODUCE ASPHALT MIXTURES

. Physical and mechanical properties of asphalt mixtures have a significant impact on a condition of fitted pavement, its stability and reliability during the entire period of its operation. These properties not only depend on bituminous binders chosen for an asphalt mixture and properties of mineral filler, but also on geometric and physical properties of the aggregate. An analysis of these indexes showed physical and geometrical indexes of aggregate of different origins (gran-ite, dolomite and gravel). While researching mineral materials used for asphalt mixtures, the values of flakiness and shape index ( FI and SI ), impact value SZ and Los Angeles coefficient LA were determined. After calculations, the hypotheses for the average of flakiness and shape indexes of researched rocks (granite, dolomite and gravel) and proximity of dispersions were tested in order to determine the authenticity of geometric quality parameters and similarity of their sampling dispersion. Results of statistical data calculations determined a correlation between geometric parameters of researched aggregate FI and SI and geometrical, strength parameters of the aggregate. The hypotheses, whether research data of these indexes were distributed by normal distribution, were tested by drawing frequency histograms of granite, dolomite and gravel flakiness and shape indexes.


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 (Petkevičius et al. 2009;Sivilevičius 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 Amšiejus et al. (2009), deformation properties developed in Amšiejus 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 (Sivilevičius, Vislavičius 2008;Mučinis et al. 2009;Mahmoud et al. 2010;Sivilevičius 2011;Vislavičius, Sivilevičius 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 (Bulevičius 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 properties 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 (Bulevičius 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.

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. 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): where: y -strength index (SZ, LA); x -geometrical index (FI, SI); a, b -const. 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.

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 fr. 4/16 were selected in accordance with the method provided in LST EN 932-1:2001 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.

Test procedure and expression of results
Flakiness index FI of crushed stone was tested in accordance with the method indicated in standard LST EN 933-3:2012. The test consisted of two screening procedures. During the first screening through square sieves, the sample was divided into narrow fractions d i /D i (where: d ithe size of the lower sieve, and D i -the size of the upper sieve). During the second screening, each particle fraction AC pavement before loads AC pavement after loads d i /D 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: where: M 1 -the sum of all the mass fractions d i /D i , expressed in grams; M 2 -the sum of all the mass fractions d i /D 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: where: M 1 -the sum of the mass of tested fractions of particles, expressed in grams; M 2 -the sum of the mass of tested fractions of non-cube-shaped particles, expressed in grams.

Fig. 3. Shape measuring calliper
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±5 g sample (10/14 mm fraction) is placed in a closed drum with ten Ø 45-49 mm steel balls and rotated 500 revolutions at 31-33 min -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: 5000 50 where: m -residue on a 1.6 mm sieve, g. Impact value SZ (as a percentage) was calculated using the following equation: where: M -the sum of the mass of particles that passed through 5 analytical sieves, expressed as a percentage.

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.

Fig. 4. Summary of results that comply with TRA MIN 07 (2007) requirements
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 ±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.

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  (6)) of geometric quality indexes: The proximity of variance and the following statistical calculations were made using Eqns (7)-(10): 1 2 ... k N n n n = + + + ; where: X , Y -compared averages of aggregate quality indexes; n, n i , m -samples of indexes (a number of chosen data for verification); 2 x s , 2 y s -variance of indexes; k -number of variable samples.
The hypotheses are tested, when significance level of the criterion is α = 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

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.
If the sample of analysed indexes n < 10, results of statistical calculations contain a very large error; therefore, statistical calculations of correlation dependence between the flakiness index FI and impact value SZ, shape index SI and the Los Angeles coefficient LA, shape index SI and impact value SZ, and the flakiness index FI and the Los Angeles coefficient LA were made according to the types of rocks without excluding the quality indexes of analysed aggregate. Statistical calculations are provided in the Table 6.
For the calculation of correlation dependences between the indexes SI and SZ, 51 samples of granite, 97 samples of dolomite and 147 samples of granite and dolomite were selected. After statistical calculation of all aggregate strains shape index SI and impact value SZ, the authors obtained correlation dependence expressed as correlation coefficient r = 0.19 for granite, r = -0.03 for dolomite and r = 0.15 for granite and dolomite -very weak dependence or no dependence at all.
After statistical calculation of granite and dolomite aggregate flakiness index FI and impact value SZ, flakiness index FI and Los Angeles coefficient LA and shape index SI and Los Angeles coefficient LA the authors determined correlation dependence expressed as correlation coefficient R interval [0.28; 0.32], e.g. weak dependence. As, therefore, calculated correlations dependence was expressed as correlation coefficient r < 0.4 (weak), it makes no sense to evaluate regression equation for these dependences.

0.74
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).

Fig. 5. Dependence between indexes FI and SI of granite, dolomite, and gravel
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 · SI with coefficient of determination R 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 · FI, coefficient of determination R 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 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 · SI, coefficient of determination R 2 = 0.39.  (Table 7). 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 α = 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.

After calculation of the statistical values only hypothesis
As all distribution of analysed indexes was stated as normal, hypothesis H o for the proximity of the flakiness index FI and shape index SI variance can be estimated.  , 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 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 1 = [0.42;0.62]) is significantly higher than analogous coefficient of gravel aggregate (g 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.