THE EFFECT OF PARTICLE ROUNDNESS ON ENGINEERING …

THE EFFECT OF PARTICLE ROUNDNESS ON ENGINEERING PARAMETERS FOR SAND Veronica Lau, Trow Associates Inc., Burnaby, British Columbia, Canada

Dawn A. Shuttle, University of British Columbia, Vancouver, British Columbia, Canada ABSTRACT The shape of particles is known to influence the engineering properties of soil. However, although the measure of the roundness of a particle is widely accepted, historically most of our understanding of the influence of particle shape has been qualitative. This study investigates the influence of particle roundness on emin, emax, and angle of repose, φrep, for two granular soils local to British Columbia: Highland Valley Copper L-L dam beach sand (HVCS), and Fraser River sand (FRS). These two sands were chosen for their specific physical properties as well as for their economic value in BC. RÉSUMÉ La forme des particules influence les propriétés mécaniques du sol. Bien que le concept de mesurer la rondeur d’une particule soit accepté, notre compréhension sur l’influence des particules n’est que qualitative. Cette étude essai d’investiguer cette influence sur emin, emax et angle de repose, φrep, pour deux types de sable trouves en Colombie Britannique : le sable de la mine Highland Valley Copper (HVCS) et le sable de la Rivière Fraser (FRS). Ces échantillons de sable ont été choisis pour leur physionomie et aussi pour leur valeur économique de la région. 1. INTRODUCTION The engineering properties of sand are dependent on the interaction between the individual particles of sand. Grain size distribution (GSD) is often used to characterize soil behaviour since this distribution affects the engineering properties of soil including void ratio and friction angle. Although the concept of measuring particle roundness (R) is not new, our understanding of the influence of particle shape on soil behaviour has been mainly qualitative. However, since the early ‘70’s interest in quantifying the effects of particle shape on the limiting void ratios, emin and emax, and angle of friction, φ, has increased considerably (Youd 1973; Miura et al. 1998; Santamarina and Cho 2004; Rousé 2005; Cho et al. 2006; among others). This study investigates the influence of particle roundness on emin, emax and angle of repose, φrep, for two sands local to British Columbia: Highland Valley Copper L-L dam beach sand (HVCS) and Fraser River sand (FRS). These two sands were chosen for their specific physical properties and for their economic value in the Province. HVCS is an angular fine-grained sand produced as waste in the extraction of copper and molybdenum at Highland Valley Copper (HVC) in the interior of BC. HVCS has been used as on-site structural fill in the development of tailings impoundments, and could be used in the design of waste cover systems in the mine reclamation process at HVC. FRS is a fine to medium sand, with variable particle shapes that range from angular to sub-rounded. The Fraser River is a major source of sand, approximately 2 x 106 m3 of sand are dredged every year by the Fraser Port Authority (Sand and Gravel News, 2006).

This sand is widely used as construction material in the Lower Mainland. FRS has been used in many bridges and roads projects, including Blundell Rd at No. 8, the Golden Ears Bridge, and the Vancouver International Airport (YVR) improvement project (Fraser Port Authority, 2005). Relations between particle roundness and void ratios found in the literature were compared with the values obtained in this study to see whether the effect of roundness on limiting void ratios is similar for engineered sands (HVCS). In addition, angles of repose reported in the literature are compared to those obtained in this study and comments are made on the trends observed. 2. APPLICATION OF ROUNDNESS TO SOIL BEHAVIOUR The amount of weathering and erosional processes to which the parent rock has been subjected to is closely reflected by the shape and size of a grain particle, also the influence that transportation processes and depositional environments have on grain size and shape is an important one. Particle roundness is important as it affects void ratio as well as the interaction between individual grain particles. Despite this fact, few studies are reported in the literature relating roundness, void ratio and/or angle of repose prior to Youd in 1973. Recently, the interest on characterising soil behaviour using grain shape has increased with contributions by Miura et al. (1998), Santamarina and Cho (2004), Rousé (2005) and Cho et al. (2006) among others.

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In his 1973 paper, Youd demonstrated that particle size in itself does not influence packing density on soils for which the Coefficient of Uniformity, Cu, ≤ 2.5; conversely particle shape greatly influences packing. Figure 1 (from Youd 1973) shows the behaviour of the limiting densities as a function of roundness having a Cu = 1.4. The definition of particle roundness used by Youd (1973) is the “ratio of the average radii of the corners of a sand grain image to the radius of the maximum circle that can be inscribed within the grain image”. This same definition has also been used by Santamarina and Cho (2004) and Rousé 2005, among others, and is computed using Equation 1 (the parameters are defined graphically in Figure 2). R = (Σri/n) / rmax [1]

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Roundness, R

Voi

d R

atio

Figure 1: Minimum and Maximum Void Ratio as a Function of Roundness (after Youd 1973)

Figure 2: Quantification of Roundness after Santamarina and Cho 2004 (Illustration taken from Rousé)

Santamarina and Cho (2004) also investigated particle shape as a factor in the behaviour of granular soils. Using a similar definition of particle roundness as Youd, they define roundness as “…the average radius of curvature of surface features relative to the radius of the maximum sphere that can be inscribed in the particle”. They also included particle sphericity (S) as another important factor influencing soil behaviour. Sphericity is defined as “…the diameter ratio between the largest inscribed and the smallest circumscribing sphere” (Santamarina and Cho 2004). Using these definitions Santamarina and Cho show the influence on packing density by platy particles. In Figure 3, Santamarina and Cho used the Sphericity and Roundness chart originated from Krumbein and Sloss (1963) to quantify S and R for grain particles according to their shape (see Figure 4).

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0

Roundness, R

Vo

id R

atio

Figure 3: Minimum and Maximum Void Ratio as a Function of Roundness (after Santamarina and Cho 2004)

Figure 4: Sphericity and Roundness (after Santamarina and Cho 2004)


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Santamarina and Cho (2004) suggested relations between the limiting void ratios emax and emin as a function of roundness for sand. emax = 0.554 + 0.154R-1 [2] emin = 0.359 + 0.082R-1 [3] The trends shown in Figure 1 and Figure 3 are the best fit lines to the measured behaviour for a selection of sands with Cu ≤ 2.5; the packing density increases as the particle roundness increases, i.e. the void ratio decreases as the particle roundness increases. Santamarina and Cho also measured the angle of repose of their sands from a cone of loose material, assuming that the angle of repose and constant volume are equivalent. They observed a reduction in φcv from 41 at R=0 to 25 at R=1 (see Figure 5). The values of Cu and D50 are not believed to influence the angle of repose (e.g. Miura et al. 1998). The angle of repose is affected by the angularity of individual grain particles, as the particle angularity increases the angle of repose increases. 3. EXPERIMENTAL TESTING As discussed earlier, two sands were tested; FRS and HVC. 3.1 Sand Description The Fraser River is the longest river in British Columbia. It starts near Mount Robson in the Rocky Mountains and flows to the Fraser River Delta in the Pacific Ocean, a distance of almost 1400km. FRS is a fine to medium sand, with variable particle shapes that range from angular to sub-rounded and displays a “salt and pepper” colour (see Photo 1). According to Chillarige et al. (1997), the average mineral composition of FRS is 40% quartz, 11% feldspar, 45% unaltered rock fragments and 4% other minerals. Our tested sample had approximately 5% biotite. Highland Valley Copper (HVC) is one of the largest open pit mines in North America. Located in the Interior of British Columbia, approximately 75km Southwest of Kamloops, HVC produces copper and molybdenum sulphide concentrates. At HVC the ore bearing rock is first crushed and then transported to the mill, where the crushed rock is subjected to two grinding stages. The second stage reduces the ore to sand particles. The produced sand is put in the floatation circuits where copper and molybdenum are extracted from the slurry. Once extraction is completed the tailings are transported to the tailings pond by means of a 7km long pipeline (Mining Technology 2006). The tailings are

10

20

30

40

50

0 0.2 0.4 0.6 0.8 1

Roundness, R

Ang

le o

f R

epos

e

Figure 5: Angle of Repose as a Function of Roundness (after Santamarina and Cho 2004)

Photo 1: Fraser River Sand (approx. 30X magnification)

Photo 2: Highland Valley Copper Sand (approx. 30X magnification)


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cycloned to sort the sand for the construction of the dam (Lighthall et al. 1989). The HVCS used in this study is from the L-L dam Beach. HVCS is a fine-grained with very angular to angular sand grains which is predominantly tan in colour (see Photo 2). 3.2 Methodology and Results 3.2.1 Sieve Analysis and Grain Size Distribution Sieve analyses were conducted on both sands using ASTM D 422-63 (2002), but a greater range of sieves were used to generate the GSD curves in order to obtain better resolution over the actual range of grain sizes. Values for Cu and the coefficient of curvature, Cc were then calculated from the D10, D30, D50 and D60 from the graphs using equations 4 and 5. Cu = D60 / D10 [4] Cc = D30 / D10 x D60 [5] The results of the GSD analyses for FRS and HVCS sand are summarized in Figure 6 and Table 1. 3.2.2 Void Ratio The minimum and maximum void ratios for both sands were determined using ASTM D 4253-00 and ASTM D4254-00 respectively. The results of the limiting void ratio and specific gravity, Gs, measurements are given in Table 2. The values obtained are the average values from three trials measuring emin and emax for each sand. 3.2.3 Roundness Photographs of sand grains were taken using a microscope to provide images of the particles large enough to measure their roundness. Circles were drawn on the photographs using a professional drafting template (see Photo 3) to measure the largest inscribed circle and to measure the average of the different radii of curvature formed by the edges of the individual sand grain. A population of twenty different grains was chosen randomly for each sand. R was then calculated using Equation 1 (from Youd 1973). The mean, the standard deviation of the sample population and the 95% confidence margin of error were calculated using MS Excel® to quantify the range of the roundness coefficient of the different sands for this study. Results for the average particle Roundness for a sample of twenty particles are shown in Table 3. The range of R values for FRS is from 0.27 to 0.63, this range of values classify FRS to be an angular to sub-angular sand. For HVCS, the range is much smaller from 0.17 to 0.33, classifying the sand to be very angular to angular.

Table 1: Sieve Analysis Summary

D60 D50 D30 D10 Cu Cc

HVCS 0.19 0.16 0.13 0.08 2.35 1.10 FRS 0.29 0.27 0.22 0.17 1.71 0.98 Table 2: emin, emax and Gs Results

Sand emin emax Gs

HVC 0.80 1.18 2.63 FRS 0.63 0.93 2.68

0

20

40

60

80

100

0.0 0.1 1.0 10.0Diameter in mm

Per

cent

Fin

er b

y W

eigh

t

HVCFRS

Figure 6: Grain Size Distribution Curves for FRS and HVCS

Photo 3: Assessing Particle Roundness for FRS Table 3: Average particle Roundness for a Sample of Twenty Particles

Sand Roundness Standard Deviation

95% Confidence Margin of Error

FRS 0.49 0.11 ± 0.05 HVCS 0.25 0.05 ± 0.02


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A qualitative assessment of R (referred to as RQual) was also conducted using Figure 4, to compare our quantitative results. The qualitative assessment was done on the same grain particles used for the quantitative assessment. Table 4 summarizes the R found for the sand particles in this study. The standard deviation calculated, shows a larger spread of R for FRS than for HVCS. This was expected as natural occurring river sand would have a larger variability than engineered sand due to the grinding methods used in the mill and to the required quality control necessary in the ore extraction processes. The Margin of error was calculated using the MS Excel®

confidence function. The mean value of the margin of error for FRS is ± 0.05 (see Table 3). This indicates that for FRS there is a good probability, with a 95% confidence, that the real mean R of the population will be 0.49 ± 0.05. The values of R evaluated quantitatively and qualitatively are comparable, with similar standard deviations and margins of error for a 95% confidence interval on the mean R. 3.2.4 Angle of Repose The ASTM C 1440-00 was used to determine φrep for the two sands. The φrep was calculated using the following formula illustrated in Photo 5. φrep = tan-1 ( 2H/ Dave – d ) [6] The calculated φrep is an average value from three trials done for the two sands. The angle of repose was calculated using equation 6 and the average of three cone diameter measurements. Table 5 shows the results. The ranges of φrep for the three sands are very small. For FRS the range is 35.6o to 35.5o and for HVCS 38.4o to 38.6o. The range was calculated using the average diameter for each trial. The average φrep was calculated using the average of the diameters for all three trials. The HVCS shows a greater angle of repose than the FRS sample. Table 4: Summary of Particle Roundness for a Sample Population of Twenty Particles

Sand Roundness Standard Deviation

95% Confidence Margin of

Error

FRS 0.49 0.11 ± 0.05

FRS Qual 0.51 0.15 ± 0.07 HVCS 0.25 0.05 ± 0.02

HVCS Qual 0.27 0.07 ± 0.03

d

H

Dave

φrep

Photo 5: Angle of Repose for FRS Table 5: Average Angle of Repose, φrep

Sand Trial 1(o) Trial 2 (o) Trial 3 (o) φrep (o)

HVC 38.6 38.4 38.4 38.5 FRS 35.6 35.5 35.6 35.6

4. DISCUSSION For FRS, the average particle size value and the Cu values obtained in this study (D50 = 0.27 and Cu = 1.71) are comparable with values stated by Chillarige et al. (1997). According to their studies of the Fraser River sand Cu = 1.7 and D50 = 0.25mm. From Cho et al. (2005), FRS Cu = 1.9 and D50 = 0.30mm. The difference in the FRS values shows the variability of the sand depending on where the sample was obtained since, as mentioned before, soil transportation and erosional process affect particle size and gradation. In addition, variations in Cu can also be imposed in order to meet the specific purpose of the researcher’s work. The values of limiting void ratios for FRS are comparable to ones found in the literature for example, the values of emin = 0.60 and emax = 1.0 with a Gs = 2.75 obtained by Chillarige et al. (1997). Achieving comparable values to those found in the literature increases confidence that proper methodology was used in this study. However, Cho (2005) found that emin = 0.78 and emax = 1.13, showing once again the variability of FRS. Figure 7 and Table 6 summarize the findings for this study. Figure 7 shows that the sands tested in this study follow the same trend suggested by Youd (1973) and by Santamarina and Cho (2004). As roundness increases, packing density increases. From Figure 7 it can be seen that the results obtained for HVCS fall between the trends proposed by Youd (1973) and Santamarina and Cho (2004). However, FRS falls above both trends. Variations in the Cu do not affect the trend.


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From Table 6, the φrep decreases as R increases. The values for φrep for HVCS and FRS of both angular to sub-angular sands, show a definite trend of φrep decreasing as R increases. Both HVCS and FRS closely follow the trend measured by Santamarina and Cho (2004) regarding the angle of repose and particle Roundness (see Figure 8). Table 6: Summary of Results

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1.2

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1.6

0.0 0.2 0.4 0.6 0.8 1.0

Roundness, R

emin

or e

max

Santamarina and Cho (2004)

Youd (1973)

HVCS FRS

Figure 7: Minimum and Maximum Void Ratio as a Function of Roundness in this Study versus Published Data

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30

40

50

0 0.2 0.4 0.6 0.8 1Roundness, R

Angle

of

Repose

Santamarina and Cho

HVCS

FRSLinear (Santamarina and Cho)

Figure 8: Angle of Repose as a Function of Roundness of HVCS and FRS

5. CONCLUSIONS The results gathered for this study follow the trends suggested and found in the literature. It is therefore concluded that the published trends for emin, emax and φrep work well, for a natural sand (i.e. FRS) and even for an engineered sand with high specific gravity (i.e. HVCS). Hence, utility may be obtained if Roundness were routinely measured for all granular soils. As particle roundness increases void ratio decreases. In addition, the angle of repose decreases as particle Roundness increases. The sands tested follow the pattern suggested by Youd (1973) and Santamarina and Cho (2004), with increased Roundness there is a decrease in void ratio, both for emin or emax (see Figure 7). Particle shape does have an influence on the limiting void ratio and angle of repose. Hence, the authors recommend measuring sand Roundness on a routine basis as a way to obtain a quick and inexpensive estimate of strength. 6. ACKNOWLEDGEMENTS The writers would like to acknowledge the contribution of a number of individuals to the paper. Highland Valley Copper Mine for providing us with the tailings sand for this study, and particularly Mr. Mark Freberg and Ms. Jaimie Dickson for making all the necessary arrangements. References ASTM D 422-63 (2002), Standard Test Method for

Particle-Size Analysis of Soils, ASTM International.

ASTM D 4253-00, Standard Test Methods for Maximum

Index Density and Unit Weight of Soils Using a

Vibratory Table, ASTM International. ASTM D 4254-00, Standard Test Method for Minimum

Index Density and Unit weight of soils and

Calculation of Relative Density, ASTM International.

ASTM C 1444-00, Standard Test Method for Measuring

the Angle of Repose of Free-Flowing Mold

Powders, ASTM International. Chillarige, A.V., Robertson, P.K., Morgenstern, N.R.,

and Christian, H.A., 1997, Evaluation of the In-situ State of the Fraser River Sand, Canadian

Geotechnical Journal, 34: 510-519. Cho, G., Dodds, J. and Santamarina C., 2006, Particle

Shape effects on Packing Density, Stiffness and Strength: Natural and Crushed Sands, Journal of

Geotechnical and Geoenvironmental Engineering, 132: 591-602.

Coduto, D.P., 1999, Geotechnical Engineering

Principles and Practices, Prentice Hall.

Sand Cu emin emax Roundness φrep (o)

HVC 2.35 0.80 1.18 0.25 38.5 FRS 1.71 0.63 0.93 0.49 35.6


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Cubrinovski, M. and Ishihara, K., 2002, Maximum and Minimum Void Ratio Characteristics of Sands, Soils and Foundations, 42(6): 65-78.

Fraser River Port Authority. Sand, MMCDA Approved. 2005. Fraser River Port Authority. March, 2006. http://www.fraserportauthority.com/sand/index.ht

Karavas, C.J. 2006. Personal communication. Lighthall, P. C., Watts, B.D., and Rice, S. 1989.

Deposition Methods for Construction of Hydraulic Tailings Dams, The Vancouver Geotechnical Society, Geotechnical Aspects of Tailings

Disposal and Acid Mine Drainage, Vancouver, May 26th, 1989.

Mining Technology. Highland Valley Copper Mine, British Columbia, Canada. 2006. Teck Cominco. March 31st, 2006. <http://www.mining-technology.com/projects/highland/>

Miura, K., Maeda, K., Furukawa, M. and Toki, S., 1998, Mechanical characteristics of sands with the different primary properties, Soils and

Foundations, 38(4): 159-172. Parks Canada. Fraser River. The Canadian heritage

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Uniformly Graded, Well-Rounded Coarse Sand, The University of British Columbia, Graduate Studies Thesis.

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Geotechnical Engineering: The Skempton

Conference, Thomas Telford, London: 604-617. Youd, T.L., 1973, Factors Controlling Maximum and

Minimum Densities of Sands, Evaluation of

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THE EFFECT OF PARTICLE ROUNDNESS ON ENGINEERING …