Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
Volume 9
Issue 4
Agricultural Engineering
Available Online: http://www.ejpau.media.pl/volume9/issue4/art-06.html


Mateusz Stasiak1, Marek Molenda1, Józef Horabik2
1 Department of Physical and Technological Properties of Agricultural Materials, Institute of Agrophysics, Polish Academy of Science, Lublin, Poland
2 Institute of Agrophysics, Polish Academy of Sciences, Lublin, Poland



Numerous branches of industry deal with granular materials such as pills and powders in the pharmaceutical and food industries or mineral powders in the construction businesses. Efficient handling and processing of large amounts of these materials require understanding of their mechanical behaviour. Process of optimization is based on knowledge of material properties that depends on properties of individual grains, interparticle friction, contact geometry and load history.

Objective of performed project was to determine and compare values of the modulus of elasticity E of rapeseeds, obtained using two methods: uniaxial compression and acoustic testing. Research was carried out for rapeseed beddings of four levels of moisture contents 6, 9, 12 and 15%. Uniaxial compression was used, as proposed by Sawicki [12]. Vertical reference pressure of 100 kPa was applied. With this method E was found to decrease from 9.0 to 6.6 MPa, with an increase in moisture content. Values of E determined using acoustic method, based on measurement of shear wave velocity, were higher then those found in uniaxial compression and decreased from 62 to 3 MPa in a range of hydrostatic pressure. Values of E from acoustic method varied in larger extent with change in moisture content and were dependant on hydrostatic pressure.

Key words: granular material, rapeseed, elasticity, modulus of elasticity, uniaxial compression, shear wave velocity.


Poland, with rapeseeds yield of 1.5 mln tones per year, is one of the leading producers in Europe. As a raw material, rapeseeds is the basic source for food and biofuel oils. It is necessary to handle and process it safety by checking the state of material during the technological process, because of great importance of the product quality for its economical value. Designer of storage systems or processing plants requires knowledge of mechanical properties, which serve as design parameters. Properties of material in bulk depend on properties of individual granules, interparticle friction, contact geometry and load history. Properties are strongly modified by moisture content, which influences the state of the seed coat as well as interior of grains. Design of an efficient technological equipment requires determination of density ρ, angle of internal friction φ, friction coefficient between material and construction material μ, modulus of elasticity E and stress ratio k.

Modulus of elasticity E characterizes elastic deformation of granular beds. Design of equipment for handling and processing of plant granular material requires experimental value of this parameter that depends on pressure [12]. Polish design standard recommends value of E related to pressure in silos that depends on height of the bed [10]. European Standard [2] recommends determination of two values of effective modulus of elasticity. One, denoted Esl measured during loading of the sample and the second Esu obtained during unloading of the sample. For calculation of values of the two modulus two ratios of change in lateral stress to change in the vertical stress are determined – Kl and Ku for loading and unloading respectively. European Standard [2] recommends determination of E in uniaxial compression test with possibility of measurement of horizontal stress and vertical strain under loads similar to those occurring in the technological process.

Strong influence of moisture content, density and porosity on E of granular materials was observed. Influence of these parameters of sand samples was examined by Liu et al. [8]. The authors reported approximately threefold change in modulus of elasticity, with varying experimental parameters. Value of E is necessary for estimation of silo loads developing with temperature variation [16]. Investigations on agricultural granular materials of Thompson & Ross [16], as well as those of Moya et al. [9], confirmed very strong influence of moisture content and pressure.

Recently, demand of industrial practice has brought about revision of several silo design codes, which included standardization of methods for determination of mechanical properties of granular materials. Standards recommend determination of mechanical properties under load condition, which are similar to the operation loads. Still determinations of some material parameters of granular beddings require standardization of equipment and methods and many laboratories around the world work on their elaboration.

Acoustic methods are widely used in various branches of science and technology. They are commonly applied for detection of internal damages in materials. Ultrasounds are also used for modifications of surface of materials [13]. Application of acoustic methods contributed to great progress in measurements of raw materials properties and products on-line, during the technological process in food industry [1]. In geotechnical applications acoustic methods have shown great advantages, while proved to be convenient and cheap tool in investigation of properties of plant granular material [5]. Application of shear waves in triaxial and uniaxial tests can provide more information about properties of plant granular materials under loads [14].


The objective of performed project was to determine and compare values of modulus of elasticity E of rapeseeds using two methods: uniaxial compression and acoustic testing based on measurement of shear wave velocity.


Modulus of elasticity E was determined for rapeseeds variety Licosmos at four levels of moisture content: 6, 9, 12 and 15%. Uniaxial compression was used as proposed by Sawicki [11], who distinguished two phases of the unloading in uniaxial compression experiment. The first phase could be used for determination of elastic constants. Figure 1 shows the scheme of the uniaxial compression apparatus that was used in testing [3].

Fig. 1. Uniaxial compression apparatus

The wall of the uniaxial compression tester consisted of two semicircular halves cut along the axis. The halves were connected with four load cells installed in pairs on the two connection lines, restoring cylindrical shape of the apparatus. One half of the wall rested directly upon the base. Bottom and top plates of the apparatus transmitted the vertical load through the load cells. The experimental set made possible for determination of the mean lateral pressure σx, mean vertical pressure on the bottom σz, and the mean vertical pressure on the top plate σz0. Surface of the wall was smooth while the surfaces of the top and bottom plates were rough. The granular material was poured into the test chamber, without vibration or other compacting action. The sample was 80 mm high and 210 mm in diameter. The bedding was loaded to the reference vertical stress σz0 of 100 kPa using universal testing machine. During compression, the top plate of the apparatus was moving down with a constant speed of 0.35 mm·min-1, while the displacement was measured with inductive transducer having accuracy of 0.01 mm. After completing compression unloading took place with the same speed of deformation until the 0 kPa of stress level was reached. Experiments were performed in three replications.

Two phases of the unloading can be distinguished (see fig. 1). During the first phase of unloading (path AB), sample shows linear reaction, which is characteristic for elastic deformation and total vertical deformation εz may be expressed as below:


where ν is Poisson’s ratio. Modulus E was determined using experimental results from linear phase of unloading. The ratio of horizontal stress σx to vertical stress σz0 was assumed constant (elastic state of stress) and a slope A of a straight line:


was estimated using linear regression procedure applied to experimental values of stresses. Then, with A estimated, values of Poisson’s ratio ν were calculated as:


Values of E were estimated using relationship εz(σz0) (equation 1) with experimental values of εz, σz0, and ν determined following equation 3.

Linear elastic theory allows calculation of elastic parameters on the basis of measured shear or longitudinal acoustic wave velocities [7]. Initial modulus can be calculated with shear wave velocity Vs and density ρ known as [17]:

         Gmax= ρVs2.            (4)

Then modulus of elasticity E of the material can be calculated [4]. Lipiński [6] determined shear wave velocity of Ottawa sand in a range of hydrostatic pressure from 50 to 400 kPa and found it increased from 150 to 300 m·s-1. Method used by Lipiński [6] was adopted in this project. Experiments were performed for ten levels of hydrostatic pressure in triaxial compression apparatus chamber fitted with piezoelements in top and bottom plates of the apparatus, that made possible generating and recording of acoustic shear waves (fig. 2).

Fig. 2. Equipment for measurement of shear wave velocity in granular material

The elastic properties were determined under load conditions similar to those encountered in industrial storage silos under typical operation regime. The material was poured into the test chamber, without vibration or other compacting action. Maximum normal pressure applied in uniaxial compression test (of 100 kPa) corresponded to pressure produced by approximately 14 m high column of grain. Measurements of shear wave velocity were conducted under hydrostatic pressure ranging from 0 to 90 kPa, that was increased in 10 kPa steps in each experiment. Hydrostatic pressure denoted 0 kPa refers to conditions at the initial state, without additional loading. The sample was cylindrical, 150 mm high and 70 mm in diameter. Measurements were performed at signal frequency of 1 kHz and amplitude of 0.6 V. Vertical deformation of the sample was measured during the experiment with inductive displacement transducer, having accuracy of 0.01 mm. Experiments were performed in three replications.


Uniaxial compression test. Figure 3 shows relationships of vertical stress σz0 and total vertical strain εz for loading – unloading cycles for rapeseed of four levels of moisture content. First part of the loading curve reflects consolidation of the sample with rearrangement of particles undergoing translation and rotation movements, but without their deformations. Second, steeper part of the curve shows an increase in the plastic and elastic stresses in the sample associated with deformation of particles.

Fig. 3. Experimental data and fitted σz 0(εz) relationships for rapeseed of four levels of moisture content

During this phase of loading deformation takes place mainly in contact areas between grains. Variation in moisture content lead to stiffness changes of particles interior and resulted in large differences between experimental stress – strain relationships.

The modulus of elasticity determined in uniaxial compression test are presented in table 1. Modulus of elasticity of rapeseed ranged from 6.6 MPa for 15% moisture content to 9 MPa for 6% moisture content. Standard deviations of modulus of elasticity were found in the range from ±0.6 MPa to ±0.9 MPa, that confirmed good repeatability of experiments as a result of repeatable internal structure of samples.

Table 1. Moduli of elasticity of rapeseed determined in uniaxial compression test and acoustic testing

Moisture content

E, MPa

E, MPa
(for ph = 90 kPa)

E a.m./E u.c.t


9.0 ± 0.6

62 ± 7



8.7 ± 0.8

58 ± 5



7.1 ± 0.6

42 ± 5



6.6 ± 0.9

40 ± 4


For a height of bed, corresponding to 100 kPa of normal pressure, Polish Standard [10] recommends applying modulus of elasticity for grain of 20 MPa, thus in good agreement with our result of uniaxial compression. Modulus of elasticity of single grain of rapeseed was examined by Stępniewski [15]. This author assumed that single grain of rapeseed is elastic spherical shell filled with uncompressible liquid and obtained modulus of elasticity equal to 6 MPa for 15% of moisture content, while for 6% of moisture content E was found of 27 MPa. Differences in values of modulus of elasticity of single grain compared to that of bedding of rapeseed result from influence of packing structure and intergranular friction.

Acoustic examination. Mean values of shear wave velocity Vs were found in a range from 50 m·s-1 to 180 m·s-1 (Fig. 4). Velocity increased with an increase in pressure ph and decreased with an increase in seeds moisture content. The highest increase in Vs, with increasing ph, from 30 to 180 m·s-1, was found in the case of rapeseeds of 6% moisture content. For seeds of 15% of m. c. wave velocity increased from approximately 50 to 140 m·s-1. The weakest variation in values of velocity, with an increase in moisture content, was observed for uncompacted samples, marked on graphs as 0 kPa. Maximum change in value of Vs of 40 m·s-1 was found for 90 kPa of hydrostatic pressure.

Fig. 4. Relationships between hydrostatic pressure ph and shear wave velocity Vs for rapeseed of four levels of moisture content

Mean values of moduli of elasticity calculated based on Vs, density and Poisson’s ratio at four levels of moisture content are presented in figure 5.

Fig. 5. Mean values of moduli of elasticity of rapeseeds of four moisture contents in a range of hydrostatic pressure from 0 to 90 kPa

Moduli of elasticity obtained with acoustic method were found higher than those obtained in uniaxial compression test. This was due to differences in ranges of sample deformation in the two tests that in the case of shear wave velocity estimation was very small (strain in an order of 10-5) as compared to deformation in uniaxial compression tests (strain of 0.12). Values of E found in uniaxial compression, similarly to those measured with acoustic method, increased with an increase in hydrostatic pressure and decreased with an increase in moisture content. No differences in values of modulus for initial state were observed, while for 90 kPa of hydrostatic pressure difference reached approximately 25 kPa. The highest values of moduli of elasticity, in a range from 10 to 62 kPa, were obtained for rapeseed of 6% of moisture content, while for 15% of m. c. E ranged from 10 to 38 kPa.

Increase in hydrostatic pressure resulted in an increase of shear wave velocity as high as ninefold in connection with an increase in number and stiffness of contacts between seeds during deformation that facilitated wave transmission. Influence of moisture content was found also strong. Increase of moisture content from 6 to 15% resulted in 25% decrease of shear wave velocity. This was a result of weakening of stiffness of contacts between particles and increase of viscosity on the contact surfaces that resulted in stronger damping of propagation of acoustic wave.

Variability of modulus of elasticity was approximately 50 kPa with an increase of hydrostatic pressure up to 90 kPa. Also Moya et al. [9] reported that vertical pressure strongly influenced values of modulus of elasticity. These authors reported that pressure increase from 14.7 to 316 kPa caused increase in E of wheat from 4.45 to 28.8 MPa, while E measured for vertical pressure of 158 kPa during the unloading phase of the same test was found of 64.3 MPa. Considerable influence of deformation velocity on measured parameters was also observed.


Values of modulus of elasticity E were found increasing with an increase in vertical pressure and decreasing with an increase in moisture content. Values obtained with two methods differed considerably probably as a result of large difference in sample strain that was in an order of 10-5 in acoustic method and in an order of 10-1 in uniaxial compression. Using values in calculations of equipment depends on strain rate in designing system.

Values of modulus of elasticity, determined in uniaxial compression test at applied reference pressure of 100 kPa were found in a range from 6.6 MPa to 9 MPa, that was in a reasonable agreement with design standards recommendations [10].

At seeds moisture content of 6% values of E estimated based on measurement of shear wave velocity were found increasing from 11 to 62 MPa with an increase in hydrostatic pressure from 10 to 90 kPa.

Values of E obtained at 90 kPa of hydrostatic pressure decreased from 62 to 40 kPa with moisture content in a range from 6 to 15%.The values of E at ph = 90 kPa from acoustic method were found maximum approximately 9 times higher than the values obtained in uniaxial compression test at 100 kPa of vertical pressure.


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Accepted for print: 10.10.2006

Mateusz Stasiak
Department of Physical and Technological Properties
of Agricultural Materials, Institute of Agrophysics,
Polish Academy of Science, Lublin, Poland
Doświadczalna 4,
P.O. Box 201, 20-290 Lublin 27, Poland
Phone: (+48) 81 743 85 58
Fax: (+48) 81 744 50 67
email: mstasiak@ipan.lublin.pl

Marek Molenda
Department of Physical and Technological Properties
of Agricultural Materials, Institute of Agrophysics,
Polish Academy of Science, Lublin, Poland
Doświadczalna 4,
P.O. Box 201, 20-290 Lublin 27, Poland

Józef Horabik
Institute of Agrophysics,
Polish Academy of Sciences, Lublin, Poland
Doświadczalna 4, 20-290 Lubln 27, Poland
phone: (+48 81) 744 50 61
fax (+48 81) 744 50 67

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