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Compressibility and equivalent bulk modulus of shelled corn
b i o s y s t e m s e n g i n e e r i n g 1 4 0 ( 2 0 1 5 ) 9 1 e9 7
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/issn/15375110
Research Paper
Compressibility and equivalent bulk modulus of shelled corn Xuduo Cheng a, Qiang Zhang b,*, Xiaojie Yan a, Cuixia Shi c a
School of Food Science and Engineering, Nanjing University of Finance and Economics, Nanjing, China Department of Biosystems Engineering, University of Manitoba, Winnipeg, Manitoba, Canada c Beijing Dongfang Fude Technology Development Center, Beijing, China b
article info
An oedometer was used to measure changes in bulk density of shelled corn at different
Article history:
compression pressures and moisture contents. An equivalent confining pressure (ECP) was
Received 5 March 2015
introduced to quantify the compression action in grain bins by considering non-uniformity
Received in revised form
and variability of compression pressures. Two models were developed for predicting bulk
9 June 2015
density and bulk modulus, respectively, as functions of ECP and moisture content. It was
Accepted 1 October 2015
found that the uncompressed bulk density of shelled corn (before applying compression
Published online 5 November 2015
pressure) decreased with grain moisture and the relationship could be adequately described by a linear equation in the moisture range from 12.6 to 17.1% wb (wet basis).
Keywords:
Shelled corn was more compressible at higher moisture content. However, bulk density
Shelled corn
approached to the same maximum value as compression pressure increased regardless of
Compression
moisture content. In other words, moisture content had little effect on the maximum
Bulk density
compressed bulk density. The equivalent bulk modulus of shelled corn increased with
Bulk modulus
compression pressure and decreased with moisture content. The predicted bulk density
Confining pressure
and bulk modulus values were in good agreement with the experimental data.
Moisture content
1.
Introduction
Shelled corn is often subject to compression in the processes of transportation, handling and storage. For example, corn in the lower portion of a storage bin is compressed due to the weight of grain above it. The compression pressure can be high enough to cause permanent deformation and cracking of grain kernels, resulting in quality problems. Furthermore, compression causes grain porosity to decrease, which may lead to increases in airflow resistance and impede aeration and drying operations. An often used indictor of grain
* Corresponding author. Tel.: þ1 204 474 9819. E-mail address: [email protected] (Q. Zhang). http://dx.doi.org/10.1016/j.biosystemseng.2015.10.001 1537-5110/© 2015 IAgrE. Published by Elsevier Ltd. All rights reserved.
© 2015 IAgrE. Published by Elsevier Ltd. All rights reserved.
compaction is (increase of) bulk density. Loewer, Ross, Kratzer, and Walker (1977) observed that bulk density varied with both the vertical pressure and moisture content (MC). Thompson and Ross (1983) measured variations in bulk density of wheat under different overburden pressures and moisture contents, and developed a set of empirical equations for predicting bulk density as a function of overburden pressure and moisture content. Cheng, Shi, and Lu (2010) used a strain-controlled triaxial apparatus to measure bulk modulus of wheat at different moistures and investigated the relationship between bulk modulus and confining pressure and moisture content. Moya, Aguado, and Ayuga (2013) conducted
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Nomenclature A Ai Abottom Aside C g H R k K K0 m MC Pa ph pi pv p ph pv p0 s1 s2 s4 V W wb 4 m r r0 rmax l Drmax DV
Cross-sectional area of oedometer sample container (m2) Area of a surface of a grain volume (m2) Cross-sectional area of grain sample (m2) jLateral area of grain sample (m2) jCompressibility Acceleration due to gravity (m s2) Height of grain sample after compression (m) Radius of oedometer sample container (m) Lateral to vertical pressure ratio Equivalent bulk modulus (EBM) (kPa) Bulk modulus number Bulk modulus exponent Moisture content (% wb) Standard atmospheric pressure (101.3 kPa) Lateral compressive pressure (stress) (kPa) Pressure acting on a surface of a grain volume (kPa) Vertical compressive pressure (stress) (kPa) Equivalent confining pressure (ECP) (kPa) Average lateral compressive pressure (stress) (kPa) Average vertical compressive pressure (stress) (kPa) Applied compression pressure on the top surface of grain (kPa) Compression pressure on the top surface of grain (kPa) Compression pressure on lateral surface of grain (kPa) Compression pressure on the bottom surface of grain (kPa) Initial volume of grain (m3) Mass of grain (kg) Wet basis Angle of internal friction (degree) Coefficient of friction of the shelled corn on the wall material of the oedometer Compressed bulk density of grain (kg m3) Uncompressed (initial) bulk density of grain (kg m3) Maximum bulk density when subject to compression (kg m3) Empirical model constant (kPa1) Maximum change in bulk density when subject to compression (kg m3) Change in grain volume (m3)
oedometer tests to determine the void ratio of several grain packings as a function of the applied vertical stress. Most studies on grain compression (packing) are experimental in nature. It is difficult to theoretically predict how grain compacts because of the complex inter-particle structure of bulk grains. Also measuring local bulk density variations in grain bins is extremely difficult. The objective of this research was to: (1) use a simple test apparatus (oedometer) to study the compression behaviour of shelled corn at different moisture
contents, and (2) develop models for predicting bulk density and bulk modulus as functions of compression pressure and moisture content.
2.
Materials and method
Shelled corn was tested at moisture contents of 12.6%, 14.7%, 15.8% and 17.1% wb. The tested corn variety was Long Gao 2, produced in Heilongjiang, China, with an oil content of 4.06% wb and initial moisture content of 12.6% wb. Higher moisture contents were achieved by the addition of water in three steps: (i) add calculated amount of distilled water to 8-kg of corn samples, (ii) place the wetted samples in sealed bags, and (iii) keep the samples in sealed bags at 15 C in an environmental chamber for a week to allow the moisture to reach equilibrium. All added water was absorbed by the grain and no visible grain deterioration (mould) was observed. The moisture content of shelled corn was determined using a standard oven-drying method by drying triplicate 10 g samples at 130 C for 19 h (ASAE, 2001). One hundred (100) kernels were randomly selected to measure the kernel size (three mutually perpendicular dimensions) using a calliper (0.01 mm resolution). The average maximum, intermedium, and the minimum dimensions were 10.19 mm (standard deviation 0.27 mm), 8.52 mm (standard deviation 0.20 mm) and 5.18 mm (standard deviation 0.16 mm), respectively. Direct shear tests were conducted to determine the angle of internal friction of the shelled corn and the coefficient of friction of the shelled corn on the wall material of the oedometer used for conducting compression tests. The direct shear tester was similar to the standard shear apparatus originally developed by Jenike for determination of flow properties, and described in more detail in Mohsenin (1986). The tester included a split square box consisting of an upper and a lower cell. To determine the internal friction, shelled corn was placed in the box (100 100 mm in crosssection, and 100 mm deep) and a vertical force was applied to the upper cell. A horizontal (shear) force was then applied to the lower cell while the upper cell was held stationary. To determine the friction coefficient of shelled corn on the metal surface, the lower cell was replaced by the metal surface, i.e., the grain contained in the upper cell rested on the metal surface and a horizontal force was then applied to the metal surface. It should be mentioned that only the original moisture content of 12.6% was tested for wall friction. The angle of internal friction and the friction coefficient were determined to be 28.0 and 0.42, respectively. The oedometer test is commonly used to measure soil consolidation properties. The oedometer test is relatively easy to perform in comparison with other tests such as the triaxial test. Researchers have used the oedometer test to determine the compressibility of various grains as a function of the applied vertical pressure (Moya, Ayuga, Guaita, & Aguado, 2002; Moya, Guaita, Aguado, & Ayuga, 2006; Moya et al., 2013). They used a standard Proctor mould, which had a diameter of 102 mm height of 122.4 mm, as per UNE 103500 (1994). A slightly larger oedometer of 138 186 mm (diameter height) was used in this study to conduct the experiment (Model LHT-1, Nanjing Soil Instruments Co.,
b i o s y s t e m s e n g i n e e r i n g 1 4 0 ( 2 0 1 5 ) 9 1 e9 7
Nanjing, China). Much research has shown that specimen size is an important factor in testing granular materials. In discussing oedometer consolidation tests, Blight (2010), chap. 4 pointed out that a general rule of selecting the specimen size was that the minimum dimension of the specimen should be at least 10 times the largest particle in the material tested. In this study, the minimum oedometer dimension of 138 mm was greater than 10 times the measured maximum corn kernel dimension of 10.19 mm. A small funnel was placed directly above the oedometer to fill the oedometer with grain. Once the oedometer was fully filled, a ruler was used to level the top surface. This method of filling produced consistent grain conditions in the oedometer (the variation in bulk density was less than 1% among three replications). After the grain sample was placed in the oedometer container, a load was applied on the top surface of the grain through a rigid disc plate and a hanging basket. The desired top pressures (50, 100, 150, 200, 250, and 300 kPa) were obtained by adding dead weights in the hanging basket. The vertical displacement (movement of the disc plate) was measured with a dial gage every 5 min in the first hour and every hour in next 11 h. It was observed that over 95% of settlement occurred within the first hour. Bulk grains are generally visco-elastoplastic and creep under a constant load. Preliminary tests were carried out to determine the time length required for grain settlement to stabilize under loading pressures of 50, 100, 150, 200, 250 and 300 kPa. After the pressure was applied, displacement (settlement) was read every hour until the change in displacement was less than 0.2% of the total displacement. Based on the results of preliminary tests, 12 h was selected for running all tests. Each test condition (a combination of moisture content and pressure) was repeated three times. The sample container of the oedometer was rigid relative to the grain. Therefore, the grain sample could not deform laterally while under vertical load. The state of stress for the sample is illustrated in Fig. 1. While the vertical stress s1 was applied on the top surface, the reactional stress s4 was induced at the bottom base, and lateral stresses s2 ¼ s3 and shear stress t on the side wall. In similar studies reported in the literature, the effect of wall friction was generally ignored, i.e., it is commonly assumed t ¼ 0, s4 ¼ s1, and s2 and s3 do not vary along the grain depth. This assumption is reasonable only if the sample container is relatively shallow, such as the
93
apparatus used by Thompson and Ross (1983) where grain was placed in a 305 305 mm square box, 103 mm deep. They expressed the density change as a function of s1 (overburden pressure). A similar approach was used by Moya et al. (2013). It is apparent that grain in an oedometer is subjected to anisotropic and variable stresses, whereas, the isotropic compression test is generally used to study the compressibility of bulk materials. In an isotropic test, the material is subjected to a uniform compressive stress (hydrostatic stress/pressure) and the critical parameter for describing the compressibility is the bulk modulus, defined as the ratio of the increase in hydrostatic pressure to the resulting relative decrease of the volume. However, grain stored in bins is subjected to vertical and lateral stresses which are different in magnitude, and this stress state in grain bins is not isotropic, but similar to that in an oedometer. Furthermore, both vertical and lateral stresses vary with grain depth in grain bins. In other words, each layer of the grain is subjected to different compression. To consider the non-uniformity (non-hydrostatic) and variability of stresses in grain bins, an equivalent confining pressure (p) was herein proposed to define an equivalent bulk modulus (K) and grain compressibility(C): P p i Ai p¼ P Ai
(1)
p ðDV=VÞ
(2)
r ¼ W=ðV DVÞ
(3)
C ¼ ðr0 rÞ=r0
(4)
K¼
The ECP may be defined for an arbitrary volume of grain in the bin, such as a layer of grain. For the stress condition in an oedometer (Fig. 1), the ECP was calculated as follows: p¼
ðs1 þ s4 ÞAbottom þ s2 Aside 2Abottom þ Aside
(5)
To determine variable stresses at different grain depths, force equilibrium on a thin layer of grain was considered (Fig. 2), and the equilibrium equation in the vertical direction was written as follows: pv A þ rgAdy 2pRkpv mdy pv þ dpv A ¼ 0
(6)
An average vertical pressure was defined as: Z
H
pv dy pv ¼
0
H
(7)
Combining Eqs. (6)e(7) and carrying out integration yielded: pv ¼
Fig. 1 e Illustration of stress state in oedometer.
2kmH rgR R rgR þ p0 1 e R 2km 2kmH 2km
(8)
The lateral to vertical pressure ratio (k-value) is commonly used to relate the lateral pressure to the vertical pressure in grain bins. Following this concept, an average lateral pressure was then calculated from the average vertical pressure (Rankine (1857):
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Fig. 2 e Force equilibrium on a layer of grain in oedometer.
vertical and lateral pressures at a grain depth could be different in different grain bins, depending on such parameters as bin geometry, grain density, internal friction of grain, and wall friction. The proposed equivalent confining pressure represented the average of vertical and lateral pressures, which were determined as a function of bin parameters. The ECP also increased slightly with the grain moisture content (Table 1). For example, the ECP was 108 kPa for 12.6% MC at applied pressure of 300 kPa vs. 110 kPa for 17.1% MC, or an increase of 1.9%. It should also be noted that the ECP was not zero when no pressure was applied on the top surface because of self-weight of grain. For a small size oedometer this pressure was not significant (about 0.3 kPa). However, the selfweight effect would be significant in full-scale grain bins.
3.2. ph ¼ kpv and k ¼
1 sin 4 1 þ sin 4
(9)
The equivalent confining pressure was finally determined as: p¼
2pv Abottom þ ph Aside Rpv þ Hph ¼ 2Abottom þ Aside RþH
(10)
It should be mentioned that two important parameters 4 and m in Eqs. (8) and (9) may vary with grain moisture. To simplify calculations, it was assumed that these two parameters were constant (28.0 and 0.42, respectively, as determined by the direct shear tests discussed earlier).
3.
Results and discussion
3.1.
Equivalent confining pressure
The equivalent confining pressure increased with the applied pressure (overburden), as expected, but was much lower than the applied pressure in magnitude (Table 1). In the previous studies of grain compression, researchers generally correlated the changes in bulk density to the applied (overburden) pressure p0 (e.g., Thompson & Ross, 1983; Moya et al., 2013). There are two potential problems of using the applied pressure as the compression pressure: (i) the volume change of a material is related to the average stress not just the stress in one direction, and (ii) under the same applied pressure, the magnitudes of
Table 1 e Equivalent confining pressures at different applied pressures and moisture contents. Applied Equivalent confining compression pressures (ECP) p (kPa) pressure 12.6% MC 14.7% MC 15.8% MC 17.1% MC p0 (kPa) 0 50 100 150 200 250 300
0.30 18.07 35.95 53.87 71.85 89.85 107.96
0.29 18.09 36.02 54.03 72.10 90.22 108.36
0.29 18.15 36.18 54.30 72.51 90.81 109.19
0.28 18.22 36.41 54.73 73.23 91.77 110.44
Measured bulk density
The initial (uncompressed) bulk density (before applying the pressure on the top surface) decreased from 771.5 to 722.1 kg m3 when the moisture content increased from 12.6% to 17.1% MC (Table 2). The similar observations of lower densities at higher moisture contents were reported by other researchers (e.g., Thompson & Ross, 1983). The relationship between the measured initial (uncompressed) bulk density and moisture content could be approximated by a linear equation (Fig. 3): r0 ¼ 931:3 11:0MC R2 ¼ 0:95
(11)
It was noticed that the higher moisture corn was more compressible than the lower moisture corn (Fig. 4). For example, the bulk density increased from 722.1 to 806.6 kg/m3, or 11.7% when a 300 kPa compression pressure was applied for 17.1% MC, whereas the corresponding change for 12.6% MC was from 771.5 to 807.3 kg/m3, or 4.6%. Thompson and Ross (1983) reported the similar trend for wheat and they attributed the larger compressibility to the higher elasticity of grain kernels with higher moisture.
3.3. Variation of bulk density with equivalent confining pressure Bulk density increased with the equivalent confining pressure, as expected, and the rate of increase was higher at lower pressure (Fig. 4). This was because most particle re-arrangement
Table 2 e Measured bulk density of shelled corn at different moisture contents. Applied pressure (kPa) 0 50 100 150 200 250 300 a
Bulk density (kg m3) 12.6% MC
14.7% MC
15.8% MC
17.1% MC
771.5 (0.2)a 786.5 (1.5) 792.4 (1.2) 796.8 (1.2) 800.6 (1.1) 804.1 (1.1) 807.3 (1.0)
758.3 (0.3) 775.3 (1.4) 783.4 (1.3) 789.5 (1.4) 794.3 (2.0) 798.5 (2.2) 801.9 (2.4)
741.2 765.8 776.0 783.2 789.4 795.5 801.2
722.1 754.0 769.3 780.0 790.5 798.1 806.6
(0.2) (0.6) (0.8) (0.8) (1.0) (1.0) (1.6)
(0.2) (1.5) (1.7) (2.0) (1.7) (1.9) (2.2)
Numbers in parentheses are standard deviations of three measurements.
95
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density was measured at a pressure (300 kPa) much higher than typical pressures in grain bins, and changes in bulk density were small at this pressure (Fig. 4). The term Drmax ð1 elp Þ reflected the observed behaviour of corn compression, i.e., the change in bulk density increased quickly with the compression pressure initially and then approached a maximum value (horizontal line) for all moisture contents (Fig. 4). To evaluate the model constant l, Eqs. (12) and (13) were combined and re-written as: r r0 ¼ elp 1 rmax r0 Fig. 3 e Variation of initial bulk density with moisture content.
occurred at the initial stage of compression. Although the initial bulk densities were different at different moisture contents, the final compressed densities differed little among the four moisture contents (ranging from 801.2 to 807.3 kg m3 or 0.8%), with no particular pattern of moisture effect. This reflected the fact that bulk density approached a stable maximum value as compression pressure increases regardless of the initial packing conditions of grain. This also indicated that moisture content affected the initial bulk density and the compressibility, but not the maximum compressed bulk density. It should be noted that the grain moisture did not change during compression tests and the density change was due to grain packing (grain kernel rearrangement and deformation). The average compressed density for the four moisture contents was 804.3 kg m3 with a standard deviation of 3.1 kg m3. Based on the above observations, the following model was proposed for predicting bulk density of shelled corn during compression: r ¼ r0 þ Drmax 1 elp
(12)
Drmax ¼ rmax r0
(13)
The initial bulk density r0 could be calculated as a function of moisture content by using Eq. (11). The average measured maximum compressed bulk density of 804.3 kg m3 could be considered as the maximum bulk density rmax because this
Fig. 4 e Variation of bulk density with equivalent confining pressure for shelled corn at moisture contents of 12.6%, 14.7%. 15.8% and 17.1% wb.
(14)
Eq. (14) was plotted in a semi-log scale (Fig. 5). The constant l was found to be 0.025 kPa1, as the slope of the regression line. It should be noted the data for all four moisture contents were pooled in plotting Fig. 5, and therefore the l value of 0.025 kPa1 was independent of moisture content. The predictions by the proposed model (Eqs. (11)e(13)) were in good agreement with the data (Fig. 4), with a maximum difference between the predicted and measured values less than 1%.
3.4.
Equivalent bulk modulus
The equivalent bulk modulus increased with the equivalent confining pressure and decreased with moisture content (Fig. 7). Variance analysis indicated that both the effects of ECP and MC were statistically significant (P < 0.05). Many researchers have used the power function to relate the bulk modulus to the confining pressure for granular materials (e.g., Pramthawee, Jongpradist, & Kongkitkul, 2011): K ¼ K0 Pa
m p Pa
(15)
It should be noted that the equivalent confining pressure was used in lieu of confining pressure s3 in this study. To determine the bulk modulus number K0 and exponent m, Eq. (15) was rewritten as: K p ¼ ln K0 þ m ln Pa Pa
(16)
By plotting Eq. (16), the bulk modulus number and exponent were determined from the intercept and slope, respectively (Fig. 7 and Table 3). It was apparent that the curves for the four moisture contents were almost parallel to each other (the slope
Fig. 5 e Relative change in bulk density as a function of equivalent confining pressure.
96
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Fig. 6 e Variation of bulk modulus with moisture content and equivalent confining pressure (predictions were based on Eqs. (15) and (17)).
Fig. 8 e Variation of bulk modulus number with equivalent confining pressure.
4.
Fig. 7 e Plot of measured bulk modulus vs. equivalent confining pressure.
varied from 0.50 to 0.53). This meant that the bulk modulus exponent (slope) was independent of moisture content, while the bulk modulus number (intercept) decreased with moisture content. The average value of exponent m was determined to be 0.51. When the bulk modulus number was plotted against moisture content, a linear relationship was observed (Fig. 8), and the following regression equation was obtained: K0 ¼ 61:7 3:0MC R2 ¼ 0:98
(17)
The predicted values of equivalent bulk modulus were in good agreement with the measured data (Fig. 6). The average differences between predicted and measured values were 3.4%, 7.1%, 3.9%, and 3.3% for 12.6%, 14.7%, 15.8%, and 17.1% moisture contents, respectively.
Table 3 e Summary of regression analysis for determining bulk modulus number K0 and exponent m. Slope m Intercept K0 R2
12.6% MC
14.7% MC
15.8% MC
17.1% MC
0.52 3.15 23.34 0.999
0.50 2.93 18.78 0.998
0.53 2.64 13.98 0.999
0.50 2.31 10.03 0.999
Conclusions
1) The uncompressed bulk density (before applying compression pressure) of shelled corn decreased with moisture content and the relationship can be adequately described by a linear equation in the moisture range from 12.6 to 17.1% wb. 2) Shelled corn was more compressible at higher moisture content. However, bulk density approached to the same maximum value as compression pressure increased regardless of moisture content. In other words, the maximum compressed bulk density of shelled corn was affected little by moisture content. 3) The equivalent bulk modulus of shelled corn increased with compression pressure and decreased with moisture content. 4) The proposed exponential model adequately predicted the variation of bulk density as a function of the equivalent confining pressure and moisture content. 5) The proposed power function model adequately predicted the variation of bulk modulus as a function of the equivalent confining pressure and moisture content.
Acknowledgement This study was funded by the National Natural Science Foundation of China (31371865) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). This research was carried out at the Modern Center of Collaboration and Innovation for Grain Circulation and Safety.
references
ASAE. (2001). ASAE S352.2 APR1988 (R2001). Moisture measurement-unground grain and seeds. American Society of Agricultural Engineers, 567e568. Blight, G. (2010). Geotechnical engineering for mine waste storage facilities. Leiden, Netherlands: CRC Press (Chapter 4).
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Cheng, X., Shi, C., & Lu, L. (2010). Measurement and experiment on bulk strain modulus of wheat. Grain Storage, 6(39), 13e18. Loewer, O. J., Jr., Ross, I. J., Kratzer, D. D., & Walker, J. N. (1977). Properties of ground shelled corn as related to forces in bulk storage structures. Transactions of the ASAE, 20(1), 155e156. Mohsenin, N. N. (1986). Physical properties of plant and animal materials (2nd ed.). New York, NY: Gordon and Breach Science Publisher. Moya, M., Aguado, P. J., & Ayuga, F. (2013). Mechanical properties of some granular agricultural materials used in silo design. International Agrophysics, 27, 181e193. http://dx.doi.org/ 10.2478/v10247-012-0084-9. Moya, M., Ayuga, F., Guaita, M., & Aguado, P. (2002). Mechanical properties of granular agricultural materials. Transactions of the ASAE, 45(5), 1569e1577.
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Moya, M., Guaita, M., Aguado, P., & Ayuga, F. (2006). Mechanical properties of granular agricultural materials, part 2. Transactions of the ASABE, 49(2), 479e489. Pramthawee, P., Jongpradist, P., & Kongkitkul, W. (2011). Evaluation of hardening soil model on numerical simulation of behaviors of high rockfill dams. Songklanakarin Journal of Science and Technology, 33(3), 325e334. Rankine, W. J. M. (1857). On the stability of loose earth. Philosophical Transactions of the Royal Society of London, 147, 9. Thompson, S. A., & Ross, I. J. (1983). Compressibility and frictional coefficients of wheat. Transactions of ASAE, 26(4), 1171e1176, 1180. UNE 103500. (1994). Geotecnia. Ensayo de compactaci on. Proctor normal [Geotechnical engineering. Compaction test. Normal Proctor]. Madrid, Spain: (AENOR).
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/issn/15375110
Research Paper
Compressibility and equivalent bulk modulus of shelled corn Xuduo Cheng a, Qiang Zhang b,*, Xiaojie Yan a, Cuixia Shi c a
School of Food Science and Engineering, Nanjing University of Finance and Economics, Nanjing, China Department of Biosystems Engineering, University of Manitoba, Winnipeg, Manitoba, Canada c Beijing Dongfang Fude Technology Development Center, Beijing, China b
article info
An oedometer was used to measure changes in bulk density of shelled corn at different
Article history:
compression pressures and moisture contents. An equivalent confining pressure (ECP) was
Received 5 March 2015
introduced to quantify the compression action in grain bins by considering non-uniformity
Received in revised form
and variability of compression pressures. Two models were developed for predicting bulk
9 June 2015
density and bulk modulus, respectively, as functions of ECP and moisture content. It was
Accepted 1 October 2015
found that the uncompressed bulk density of shelled corn (before applying compression
Published online 5 November 2015
pressure) decreased with grain moisture and the relationship could be adequately described by a linear equation in the moisture range from 12.6 to 17.1% wb (wet basis).
Keywords:
Shelled corn was more compressible at higher moisture content. However, bulk density
Shelled corn
approached to the same maximum value as compression pressure increased regardless of
Compression
moisture content. In other words, moisture content had little effect on the maximum
Bulk density
compressed bulk density. The equivalent bulk modulus of shelled corn increased with
Bulk modulus
compression pressure and decreased with moisture content. The predicted bulk density
Confining pressure
and bulk modulus values were in good agreement with the experimental data.
Moisture content
1.
Introduction
Shelled corn is often subject to compression in the processes of transportation, handling and storage. For example, corn in the lower portion of a storage bin is compressed due to the weight of grain above it. The compression pressure can be high enough to cause permanent deformation and cracking of grain kernels, resulting in quality problems. Furthermore, compression causes grain porosity to decrease, which may lead to increases in airflow resistance and impede aeration and drying operations. An often used indictor of grain
* Corresponding author. Tel.: þ1 204 474 9819. E-mail address: [email protected] (Q. Zhang). http://dx.doi.org/10.1016/j.biosystemseng.2015.10.001 1537-5110/© 2015 IAgrE. Published by Elsevier Ltd. All rights reserved.
© 2015 IAgrE. Published by Elsevier Ltd. All rights reserved.
compaction is (increase of) bulk density. Loewer, Ross, Kratzer, and Walker (1977) observed that bulk density varied with both the vertical pressure and moisture content (MC). Thompson and Ross (1983) measured variations in bulk density of wheat under different overburden pressures and moisture contents, and developed a set of empirical equations for predicting bulk density as a function of overburden pressure and moisture content. Cheng, Shi, and Lu (2010) used a strain-controlled triaxial apparatus to measure bulk modulus of wheat at different moistures and investigated the relationship between bulk modulus and confining pressure and moisture content. Moya, Aguado, and Ayuga (2013) conducted
92
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Nomenclature A Ai Abottom Aside C g H R k K K0 m MC Pa ph pi pv p ph pv p0 s1 s2 s4 V W wb 4 m r r0 rmax l Drmax DV
Cross-sectional area of oedometer sample container (m2) Area of a surface of a grain volume (m2) Cross-sectional area of grain sample (m2) jLateral area of grain sample (m2) jCompressibility Acceleration due to gravity (m s2) Height of grain sample after compression (m) Radius of oedometer sample container (m) Lateral to vertical pressure ratio Equivalent bulk modulus (EBM) (kPa) Bulk modulus number Bulk modulus exponent Moisture content (% wb) Standard atmospheric pressure (101.3 kPa) Lateral compressive pressure (stress) (kPa) Pressure acting on a surface of a grain volume (kPa) Vertical compressive pressure (stress) (kPa) Equivalent confining pressure (ECP) (kPa) Average lateral compressive pressure (stress) (kPa) Average vertical compressive pressure (stress) (kPa) Applied compression pressure on the top surface of grain (kPa) Compression pressure on the top surface of grain (kPa) Compression pressure on lateral surface of grain (kPa) Compression pressure on the bottom surface of grain (kPa) Initial volume of grain (m3) Mass of grain (kg) Wet basis Angle of internal friction (degree) Coefficient of friction of the shelled corn on the wall material of the oedometer Compressed bulk density of grain (kg m3) Uncompressed (initial) bulk density of grain (kg m3) Maximum bulk density when subject to compression (kg m3) Empirical model constant (kPa1) Maximum change in bulk density when subject to compression (kg m3) Change in grain volume (m3)
oedometer tests to determine the void ratio of several grain packings as a function of the applied vertical stress. Most studies on grain compression (packing) are experimental in nature. It is difficult to theoretically predict how grain compacts because of the complex inter-particle structure of bulk grains. Also measuring local bulk density variations in grain bins is extremely difficult. The objective of this research was to: (1) use a simple test apparatus (oedometer) to study the compression behaviour of shelled corn at different moisture
contents, and (2) develop models for predicting bulk density and bulk modulus as functions of compression pressure and moisture content.
2.
Materials and method
Shelled corn was tested at moisture contents of 12.6%, 14.7%, 15.8% and 17.1% wb. The tested corn variety was Long Gao 2, produced in Heilongjiang, China, with an oil content of 4.06% wb and initial moisture content of 12.6% wb. Higher moisture contents were achieved by the addition of water in three steps: (i) add calculated amount of distilled water to 8-kg of corn samples, (ii) place the wetted samples in sealed bags, and (iii) keep the samples in sealed bags at 15 C in an environmental chamber for a week to allow the moisture to reach equilibrium. All added water was absorbed by the grain and no visible grain deterioration (mould) was observed. The moisture content of shelled corn was determined using a standard oven-drying method by drying triplicate 10 g samples at 130 C for 19 h (ASAE, 2001). One hundred (100) kernels were randomly selected to measure the kernel size (three mutually perpendicular dimensions) using a calliper (0.01 mm resolution). The average maximum, intermedium, and the minimum dimensions were 10.19 mm (standard deviation 0.27 mm), 8.52 mm (standard deviation 0.20 mm) and 5.18 mm (standard deviation 0.16 mm), respectively. Direct shear tests were conducted to determine the angle of internal friction of the shelled corn and the coefficient of friction of the shelled corn on the wall material of the oedometer used for conducting compression tests. The direct shear tester was similar to the standard shear apparatus originally developed by Jenike for determination of flow properties, and described in more detail in Mohsenin (1986). The tester included a split square box consisting of an upper and a lower cell. To determine the internal friction, shelled corn was placed in the box (100 100 mm in crosssection, and 100 mm deep) and a vertical force was applied to the upper cell. A horizontal (shear) force was then applied to the lower cell while the upper cell was held stationary. To determine the friction coefficient of shelled corn on the metal surface, the lower cell was replaced by the metal surface, i.e., the grain contained in the upper cell rested on the metal surface and a horizontal force was then applied to the metal surface. It should be mentioned that only the original moisture content of 12.6% was tested for wall friction. The angle of internal friction and the friction coefficient were determined to be 28.0 and 0.42, respectively. The oedometer test is commonly used to measure soil consolidation properties. The oedometer test is relatively easy to perform in comparison with other tests such as the triaxial test. Researchers have used the oedometer test to determine the compressibility of various grains as a function of the applied vertical pressure (Moya, Ayuga, Guaita, & Aguado, 2002; Moya, Guaita, Aguado, & Ayuga, 2006; Moya et al., 2013). They used a standard Proctor mould, which had a diameter of 102 mm height of 122.4 mm, as per UNE 103500 (1994). A slightly larger oedometer of 138 186 mm (diameter height) was used in this study to conduct the experiment (Model LHT-1, Nanjing Soil Instruments Co.,
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Nanjing, China). Much research has shown that specimen size is an important factor in testing granular materials. In discussing oedometer consolidation tests, Blight (2010), chap. 4 pointed out that a general rule of selecting the specimen size was that the minimum dimension of the specimen should be at least 10 times the largest particle in the material tested. In this study, the minimum oedometer dimension of 138 mm was greater than 10 times the measured maximum corn kernel dimension of 10.19 mm. A small funnel was placed directly above the oedometer to fill the oedometer with grain. Once the oedometer was fully filled, a ruler was used to level the top surface. This method of filling produced consistent grain conditions in the oedometer (the variation in bulk density was less than 1% among three replications). After the grain sample was placed in the oedometer container, a load was applied on the top surface of the grain through a rigid disc plate and a hanging basket. The desired top pressures (50, 100, 150, 200, 250, and 300 kPa) were obtained by adding dead weights in the hanging basket. The vertical displacement (movement of the disc plate) was measured with a dial gage every 5 min in the first hour and every hour in next 11 h. It was observed that over 95% of settlement occurred within the first hour. Bulk grains are generally visco-elastoplastic and creep under a constant load. Preliminary tests were carried out to determine the time length required for grain settlement to stabilize under loading pressures of 50, 100, 150, 200, 250 and 300 kPa. After the pressure was applied, displacement (settlement) was read every hour until the change in displacement was less than 0.2% of the total displacement. Based on the results of preliminary tests, 12 h was selected for running all tests. Each test condition (a combination of moisture content and pressure) was repeated three times. The sample container of the oedometer was rigid relative to the grain. Therefore, the grain sample could not deform laterally while under vertical load. The state of stress for the sample is illustrated in Fig. 1. While the vertical stress s1 was applied on the top surface, the reactional stress s4 was induced at the bottom base, and lateral stresses s2 ¼ s3 and shear stress t on the side wall. In similar studies reported in the literature, the effect of wall friction was generally ignored, i.e., it is commonly assumed t ¼ 0, s4 ¼ s1, and s2 and s3 do not vary along the grain depth. This assumption is reasonable only if the sample container is relatively shallow, such as the
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apparatus used by Thompson and Ross (1983) where grain was placed in a 305 305 mm square box, 103 mm deep. They expressed the density change as a function of s1 (overburden pressure). A similar approach was used by Moya et al. (2013). It is apparent that grain in an oedometer is subjected to anisotropic and variable stresses, whereas, the isotropic compression test is generally used to study the compressibility of bulk materials. In an isotropic test, the material is subjected to a uniform compressive stress (hydrostatic stress/pressure) and the critical parameter for describing the compressibility is the bulk modulus, defined as the ratio of the increase in hydrostatic pressure to the resulting relative decrease of the volume. However, grain stored in bins is subjected to vertical and lateral stresses which are different in magnitude, and this stress state in grain bins is not isotropic, but similar to that in an oedometer. Furthermore, both vertical and lateral stresses vary with grain depth in grain bins. In other words, each layer of the grain is subjected to different compression. To consider the non-uniformity (non-hydrostatic) and variability of stresses in grain bins, an equivalent confining pressure (p) was herein proposed to define an equivalent bulk modulus (K) and grain compressibility(C): P p i Ai p¼ P Ai
(1)
p ðDV=VÞ
(2)
r ¼ W=ðV DVÞ
(3)
C ¼ ðr0 rÞ=r0
(4)
K¼
The ECP may be defined for an arbitrary volume of grain in the bin, such as a layer of grain. For the stress condition in an oedometer (Fig. 1), the ECP was calculated as follows: p¼
ðs1 þ s4 ÞAbottom þ s2 Aside 2Abottom þ Aside
(5)
To determine variable stresses at different grain depths, force equilibrium on a thin layer of grain was considered (Fig. 2), and the equilibrium equation in the vertical direction was written as follows: pv A þ rgAdy 2pRkpv mdy pv þ dpv A ¼ 0
(6)
An average vertical pressure was defined as: Z
H
pv dy pv ¼
0
H
(7)
Combining Eqs. (6)e(7) and carrying out integration yielded: pv ¼
Fig. 1 e Illustration of stress state in oedometer.
2kmH rgR R rgR þ p0 1 e R 2km 2kmH 2km
(8)
The lateral to vertical pressure ratio (k-value) is commonly used to relate the lateral pressure to the vertical pressure in grain bins. Following this concept, an average lateral pressure was then calculated from the average vertical pressure (Rankine (1857):
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Fig. 2 e Force equilibrium on a layer of grain in oedometer.
vertical and lateral pressures at a grain depth could be different in different grain bins, depending on such parameters as bin geometry, grain density, internal friction of grain, and wall friction. The proposed equivalent confining pressure represented the average of vertical and lateral pressures, which were determined as a function of bin parameters. The ECP also increased slightly with the grain moisture content (Table 1). For example, the ECP was 108 kPa for 12.6% MC at applied pressure of 300 kPa vs. 110 kPa for 17.1% MC, or an increase of 1.9%. It should also be noted that the ECP was not zero when no pressure was applied on the top surface because of self-weight of grain. For a small size oedometer this pressure was not significant (about 0.3 kPa). However, the selfweight effect would be significant in full-scale grain bins.
3.2. ph ¼ kpv and k ¼
1 sin 4 1 þ sin 4
(9)
The equivalent confining pressure was finally determined as: p¼
2pv Abottom þ ph Aside Rpv þ Hph ¼ 2Abottom þ Aside RþH
(10)
It should be mentioned that two important parameters 4 and m in Eqs. (8) and (9) may vary with grain moisture. To simplify calculations, it was assumed that these two parameters were constant (28.0 and 0.42, respectively, as determined by the direct shear tests discussed earlier).
3.
Results and discussion
3.1.
Equivalent confining pressure
The equivalent confining pressure increased with the applied pressure (overburden), as expected, but was much lower than the applied pressure in magnitude (Table 1). In the previous studies of grain compression, researchers generally correlated the changes in bulk density to the applied (overburden) pressure p0 (e.g., Thompson & Ross, 1983; Moya et al., 2013). There are two potential problems of using the applied pressure as the compression pressure: (i) the volume change of a material is related to the average stress not just the stress in one direction, and (ii) under the same applied pressure, the magnitudes of
Table 1 e Equivalent confining pressures at different applied pressures and moisture contents. Applied Equivalent confining compression pressures (ECP) p (kPa) pressure 12.6% MC 14.7% MC 15.8% MC 17.1% MC p0 (kPa) 0 50 100 150 200 250 300
0.30 18.07 35.95 53.87 71.85 89.85 107.96
0.29 18.09 36.02 54.03 72.10 90.22 108.36
0.29 18.15 36.18 54.30 72.51 90.81 109.19
0.28 18.22 36.41 54.73 73.23 91.77 110.44
Measured bulk density
The initial (uncompressed) bulk density (before applying the pressure on the top surface) decreased from 771.5 to 722.1 kg m3 when the moisture content increased from 12.6% to 17.1% MC (Table 2). The similar observations of lower densities at higher moisture contents were reported by other researchers (e.g., Thompson & Ross, 1983). The relationship between the measured initial (uncompressed) bulk density and moisture content could be approximated by a linear equation (Fig. 3): r0 ¼ 931:3 11:0MC R2 ¼ 0:95
(11)
It was noticed that the higher moisture corn was more compressible than the lower moisture corn (Fig. 4). For example, the bulk density increased from 722.1 to 806.6 kg/m3, or 11.7% when a 300 kPa compression pressure was applied for 17.1% MC, whereas the corresponding change for 12.6% MC was from 771.5 to 807.3 kg/m3, or 4.6%. Thompson and Ross (1983) reported the similar trend for wheat and they attributed the larger compressibility to the higher elasticity of grain kernels with higher moisture.
3.3. Variation of bulk density with equivalent confining pressure Bulk density increased with the equivalent confining pressure, as expected, and the rate of increase was higher at lower pressure (Fig. 4). This was because most particle re-arrangement
Table 2 e Measured bulk density of shelled corn at different moisture contents. Applied pressure (kPa) 0 50 100 150 200 250 300 a
Bulk density (kg m3) 12.6% MC
14.7% MC
15.8% MC
17.1% MC
771.5 (0.2)a 786.5 (1.5) 792.4 (1.2) 796.8 (1.2) 800.6 (1.1) 804.1 (1.1) 807.3 (1.0)
758.3 (0.3) 775.3 (1.4) 783.4 (1.3) 789.5 (1.4) 794.3 (2.0) 798.5 (2.2) 801.9 (2.4)
741.2 765.8 776.0 783.2 789.4 795.5 801.2
722.1 754.0 769.3 780.0 790.5 798.1 806.6
(0.2) (0.6) (0.8) (0.8) (1.0) (1.0) (1.6)
(0.2) (1.5) (1.7) (2.0) (1.7) (1.9) (2.2)
Numbers in parentheses are standard deviations of three measurements.
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density was measured at a pressure (300 kPa) much higher than typical pressures in grain bins, and changes in bulk density were small at this pressure (Fig. 4). The term Drmax ð1 elp Þ reflected the observed behaviour of corn compression, i.e., the change in bulk density increased quickly with the compression pressure initially and then approached a maximum value (horizontal line) for all moisture contents (Fig. 4). To evaluate the model constant l, Eqs. (12) and (13) were combined and re-written as: r r0 ¼ elp 1 rmax r0 Fig. 3 e Variation of initial bulk density with moisture content.
occurred at the initial stage of compression. Although the initial bulk densities were different at different moisture contents, the final compressed densities differed little among the four moisture contents (ranging from 801.2 to 807.3 kg m3 or 0.8%), with no particular pattern of moisture effect. This reflected the fact that bulk density approached a stable maximum value as compression pressure increases regardless of the initial packing conditions of grain. This also indicated that moisture content affected the initial bulk density and the compressibility, but not the maximum compressed bulk density. It should be noted that the grain moisture did not change during compression tests and the density change was due to grain packing (grain kernel rearrangement and deformation). The average compressed density for the four moisture contents was 804.3 kg m3 with a standard deviation of 3.1 kg m3. Based on the above observations, the following model was proposed for predicting bulk density of shelled corn during compression: r ¼ r0 þ Drmax 1 elp
(12)
Drmax ¼ rmax r0
(13)
The initial bulk density r0 could be calculated as a function of moisture content by using Eq. (11). The average measured maximum compressed bulk density of 804.3 kg m3 could be considered as the maximum bulk density rmax because this
Fig. 4 e Variation of bulk density with equivalent confining pressure for shelled corn at moisture contents of 12.6%, 14.7%. 15.8% and 17.1% wb.
(14)
Eq. (14) was plotted in a semi-log scale (Fig. 5). The constant l was found to be 0.025 kPa1, as the slope of the regression line. It should be noted the data for all four moisture contents were pooled in plotting Fig. 5, and therefore the l value of 0.025 kPa1 was independent of moisture content. The predictions by the proposed model (Eqs. (11)e(13)) were in good agreement with the data (Fig. 4), with a maximum difference between the predicted and measured values less than 1%.
3.4.
Equivalent bulk modulus
The equivalent bulk modulus increased with the equivalent confining pressure and decreased with moisture content (Fig. 7). Variance analysis indicated that both the effects of ECP and MC were statistically significant (P < 0.05). Many researchers have used the power function to relate the bulk modulus to the confining pressure for granular materials (e.g., Pramthawee, Jongpradist, & Kongkitkul, 2011): K ¼ K0 Pa
m p Pa
(15)
It should be noted that the equivalent confining pressure was used in lieu of confining pressure s3 in this study. To determine the bulk modulus number K0 and exponent m, Eq. (15) was rewritten as: K p ¼ ln K0 þ m ln Pa Pa
(16)
By plotting Eq. (16), the bulk modulus number and exponent were determined from the intercept and slope, respectively (Fig. 7 and Table 3). It was apparent that the curves for the four moisture contents were almost parallel to each other (the slope
Fig. 5 e Relative change in bulk density as a function of equivalent confining pressure.
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Fig. 6 e Variation of bulk modulus with moisture content and equivalent confining pressure (predictions were based on Eqs. (15) and (17)).
Fig. 8 e Variation of bulk modulus number with equivalent confining pressure.
4.
Fig. 7 e Plot of measured bulk modulus vs. equivalent confining pressure.
varied from 0.50 to 0.53). This meant that the bulk modulus exponent (slope) was independent of moisture content, while the bulk modulus number (intercept) decreased with moisture content. The average value of exponent m was determined to be 0.51. When the bulk modulus number was plotted against moisture content, a linear relationship was observed (Fig. 8), and the following regression equation was obtained: K0 ¼ 61:7 3:0MC R2 ¼ 0:98
(17)
The predicted values of equivalent bulk modulus were in good agreement with the measured data (Fig. 6). The average differences between predicted and measured values were 3.4%, 7.1%, 3.9%, and 3.3% for 12.6%, 14.7%, 15.8%, and 17.1% moisture contents, respectively.
Table 3 e Summary of regression analysis for determining bulk modulus number K0 and exponent m. Slope m Intercept K0 R2
12.6% MC
14.7% MC
15.8% MC
17.1% MC
0.52 3.15 23.34 0.999
0.50 2.93 18.78 0.998
0.53 2.64 13.98 0.999
0.50 2.31 10.03 0.999
Conclusions
1) The uncompressed bulk density (before applying compression pressure) of shelled corn decreased with moisture content and the relationship can be adequately described by a linear equation in the moisture range from 12.6 to 17.1% wb. 2) Shelled corn was more compressible at higher moisture content. However, bulk density approached to the same maximum value as compression pressure increased regardless of moisture content. In other words, the maximum compressed bulk density of shelled corn was affected little by moisture content. 3) The equivalent bulk modulus of shelled corn increased with compression pressure and decreased with moisture content. 4) The proposed exponential model adequately predicted the variation of bulk density as a function of the equivalent confining pressure and moisture content. 5) The proposed power function model adequately predicted the variation of bulk modulus as a function of the equivalent confining pressure and moisture content.
Acknowledgement This study was funded by the National Natural Science Foundation of China (31371865) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). This research was carried out at the Modern Center of Collaboration and Innovation for Grain Circulation and Safety.
references
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