Friction Angles of Sands: An Appraisal

River sand is a naturally occurring conventional construction material, which has good frictional properties. Due to a steep rise in the construction activities all over the world, natural sand resources are getting depleted. This has favored / forced the construction industry in general and geotechnical engineering practice in particular to go for manufactured sands (M-sands). This necessitates a proper understanding of the frictional characteristics of M–sands. In this technical note, the results from a comparative study of the friction angles of river sand and M-sand with reference to the effect of grain size, grain angularity, dry density and gradation are reported. It is shown that M-sand exhibits higher friction angles than river sand at minimum density levels and river sand exhibits higher friction angles than M-sand at maximum density levels, on average, irrespective of grain size. It is also shown that poorly graded M-sands exhibit higher friction angles than well graded M-sands at minimum density levels, whereas well graded river sands have higher friction angles than poorly graded river sands irrespective of density levels.


Introduction
The shear strength of granular materials such as sands is primarily due to their angle of internal friction or friction angle (φ).Various factors that might affect the friction angles of sands include particle size, grain angularity / grain shape, gradation and dry density.Islam et al. (2011) and Kara et al. (2013) studied the contribution of particle size to friction angle.They concluded that the peak friction angle would increase with the increase in the grain size.However, studies of Vangla and Latha (2015) indicated that the peak shear strengths were unaffected by the grain size of the sands at same void ratio level.The studies of Wen et al. (2018) revealed that the shear strength increased with increase in the maximum grain size in the sample.Shin and Santamarina (2013) showed that the friction angle would increase with an increase in the mass fraction of angular particles.Stark et al. (2014) showed that the elliptic, plate-like shape of beach sand increased the angles of internal friction of both pure sand and sand-gravel mixtures.Lu et al. (2019) have studies the impact of Vol:.( 1234567890) particle shape on physical and mechanical properties of poorly graded sandy soils.They have noticed that sand with rounded particles has a greater peak shear strength than sand with angular particles, when the normal stress is less than 200 kPa and no noticeable difference in their critical shear strengths.
Due to the over exploitation of natural sands by the construction industry, good natural sands are becoming scarce.With the result, it has become the necessity of the day to use alternate granular materials such as rock flour or manufactured sand (i.e., M-sand).In the light of contradictions noticed by earlier researchers, this note attempts to bring out the effect of grain size, gradation and initial dry density on the friction angles of conventional sands and M-sand.

Materials and Methods
River sand used in this study was collected from the bank of river Cauvery in T.Narasipur, Mysuru district, Karnataka state, India.M-sand used in this work was procured from one of the private M-sand manufacturing units near Mysuru city, Karnataka state, India, where the granitic rocks are processed.The collected river sand and M-sand were cleaned, dried and sieved to obtain particles of different size ranges and gradation required.They were stored in separate bins.
Dry sieve analysis was conducted on samples of both river sands and M-sands so obtained to determine their gradation characteristics namely, coefficient of uniformity (C u ) and coefficient of curvature (C c ) (Table 1) (IS 2720-Part 4, 1985).These coefficients are defined as below. (1) where, D 10 , D 30 and D 60 represent the equivalent diameters of the particles corresponding to 10%, 30% and 60% finer respectively.In order to study the effect of gradation of sands on their friction angles, bulk samples of well graded river sand / M-sand were prepared from the samples of river sand and M-sand collected.While doing so, care was taken to see that the gradation characteristics of both well graded samples of river sand and M-sand remain the same (Fig. 1) (Table 2).
In order to study the effect of initial dry density level on the friction angle, the maximum and minimum dry densities for the sand / M-sand samples were determined.The minimum dry density was found by pouring device method (IS 2720-Part 14, 1983).The maximum dry density was found by dry vibration method as indicated below.

Determination of Maximum Dry Density
• A metallic mould was taken, cleaned and dried.
Knowing its internal diameter and height, the volume of the mould was calculated.The empty mass of the mould was recorded.• A collar was attached to the mould.
• The mould was placed on the vibrating deck and fixed to it with nuts and bolts.• The mould was filled with the dry sand sample in three layers.• The vibrator was allowed to run for 8 min.
• The collar was removed; Excess sand was struck off using a straight edge.The combined mass of the mould and the sand sample in it was noted.• Using the mass of the sand filling the mould and the volume of the mould, the dry density of the sand was calculated.• The average of three trials was recorded as the maximum dry density of the sand sample.Not much difference was noticed among the results from the three trials.
The values of maximum and minimum dry densities of all the samples of river sand and M-sand are listed in Table 3.The angularity of the sand grains was judged by visual observation.

Determination of Friction Angle
Shear box tests were conducted on dry river sand and M-sand samples at constant initial dry density levels (either maximum or minimum dry density  values listed in Table 3-indicated as the taken values in Tables 4, 5 and 6) (IS: 2720, Part-13, 1986).When the normal stresses were applied on the samples, the densities of the samples were observed to increase slightly.These increased densities have been indicated as the realized values in Tables 4, 5 and 6.The shearing was done at a constant strain rate of 1.25 mm / minute.In order to check if any dilation takes place during testing, arrangements were made to observe vertical deformations of the sample in the shear box during the testing process with the help of a dial gauge.Shear stress v/s strain relationships were plotted under each of the applied normal stress on the sample (i.e., 25 kN/m 2 , 50 kN/ m 2 , 100 kN/m 2 , 150 kN/m 2 and 200 kN/m 2 ) from which peak/failure shear stresses were noted.When the normal stress was applied, the actual initial dry density realized was determined by measuring the vertical compression of the sample under the applied normal stress using a dial gauge.The applied normal stresses and the corresponding peak / failure shear stresses were used to plot the strength envelops, from which friction angles were obtained.

Results and Discussions
Tables 4 and 5 present the results from the shear box tests conducted on dry samples of poorly graded river sands and M-sands.Table 6 presents the results from the shear box tests conducted on dry samples of well graded river sand and M-sand samples.During testing, no dilation of the samples was observed.

Effect of Grain Size
Figures 2 and 3 present the variation of friction angle with minimum grain size in the sample for poorly graded river sand and M-sand respectively.They also show the effect of dry density on the friction angle.
The following observations can be made from these figures common to both river sand and M-sand.
• The friction angles at any dry density level vary with the grain size.This observation is noted to be somewhat different from those observed by Islam et al. ( 2011) and Kara et al. (2013) as explained in the following paragraphs.• The friction angles also vary with dry density level.
The following differentiating observations can be made between river sands and M-sands studied.
• The friction angles of river sand vary over a very narrow range of 36°-40° beyond about 0.2 mm grain size, irrespective of dry density level.However, the friction angles of M-sand vary quite appreciably with the grain size, at the maximum dry density level in particular.• The friction angle of river sand decreases with increase in the grain size on an average to reach a near constant value (37° on average) at maximum dry density level, whereas it increases with increase in the grain size on an average to reach a near constant value (38° on average) at minimum dry density level.• While the friction angles of river sand at higher grain size ranges at minimum dry density level are more than those at maximum dry density level, those of M-sand at minimum dry density level are more than those at maximum dry density level for all grain size ranges.

Effect of Angularity
Figures 4 and 5 present the effect of angularity of the grains on the friction angle with regard to poorly graded river sand and M-sand respectively.It can be seen that.Grain size in mm River Sand ( Maximum dry density ) River Sand ( Minimum dry density ) • The sub rounded river sands have higher friction angles than the angular M-sands on an average at maximum dry density level.Lu et al. (2019) noticed similar type of behavior, however at lower normal stresses.During shearing at maximum dry density levels, the relatively smooth surfaced river sand grains can move relative to each other with more contact area leading to higher friction angles.• The reverse trend can be seen at minimum dry density level.At minimum dry density levels, the angular grains of M-sand can also move relative to each other.Due to the interlocking of grains, they will be able to mobilize higher friction angles than relatively smooth surfaced river sand grains.
Study of the results listed in Table 6 indicates the effect of angularity in the case of well graded sands.Well graded M-sands with angular grains show higher friction angles than the relatively smooth surfaced well graded river sands at minimum dry density levels.

Effect of Gradation
It is normally accepted that the well graded sands exhibit higher friction angles than the poorly graded sands.The study of the results presented in Tables 4, 5 and 6 indicate that such a generalization may be valid at maximum dry density levels.At minimum dry density levels, even poorly graded M-sands may have higher friction angles due to their grain angularity.

Conclusions
The present work has dealt with a comparative study of the friction angles of the naturally available river sands and manufactured sands.The factors considered in this study were the size, initial dry density level, grain angularity and gradation of the grains.Following major conclusions can be drawn from this study.
• The initial dry density levels have appreciable influence on the friction angles of sands.While the river sands exhibit higher friction angles over M-sands at the maximum dry density levels, M-sands show higher friction angles over river sands at minimum dry density levels.• The friction angles tend to reach a near constant range at higher grain sizes for river sands whereas the friction angles of M-sands vary appreciably with the grain size.• Initial dry density levels have a masking effect over the effect of grain angularity on the friction angles.• Well graded sand samples have higher friction angles than the poorly graded sands.However, poorly graded M-sands may have higher friction angles than well graded M-sands due to their grain angularity at minimum dry density levels.
In view of the scarcity of river sands, there is a growing tendency to use M-sands in practice.The results of the present study indicate that M-sands can replace river sands in practice where frictional characteristics dominate the requirement as they exhibit comparable

Fig. 1
Fig. 1 Particle size distribution of well graded river sand and M-sand

Fig. 2
Fig. 2 Effect of grain size on friction angle: River sand

Fig. 3
Fig. 3 Effect of grain size on friction angle: M-sand

Fig. 5
Fig. 5 Effect of grain angularity on friction angle at minimum dry density level

Table 2
Composition and gradation characteristics of well graded river sand and M-sand

Table 4
The details of the test results corresponding to river sand of different size range