E3S Web of Conferences 415, 01011 (2023)
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https://doi.org/10.1051/e3sconf/202341501011

The influence of particle size on the spread distance and angle offriction of granular materials
Chyan-Deng Jan, and Litan Dey*
Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Taiwan

Abstract. To produce a hazard map and thus provide mitigation measures against natural catastrophic events such aslandslides, avalanches, and debris flows, it is necessary to determine the spread distance of such flows. There is awell-documented relationship between the angle of friction and the debris flow volume, allowing one to determine
the possible distance a debris flow can travel. However, the effect of mean particle size (𝑑50 ) and the sorting
coefficient (𝑆𝑐 ) on the final spread distance (𝐷𝑓 ) has received mere attention. In this study, a mini conical-shaped
mould was used to measure the final spread distance (𝐷𝑓 ) and angle of friction (𝛼𝑓 ) for various dry granular material
samples both in air and in water. Experimental results indicated that a granular material sample with a smaller 𝑑50
travel a longer distance compared to a sample with a higher 𝑑50 . However, a sample with a smaller 𝑑50 results in asmaller angle of friction than the one with a higher 𝑑50 . Conversely, a well-sorted sample has a smaller spread
distance and larger angle of friction. Results also indicated that the spread distance in air is slightly larger and theangle of friction is slightly smaller than in water.

1 Introduction
Granular flows, propelled by gravity, occur often on thesurfaces of Earth and other planets. They are composed ofsolid particles that have been often mixed with an interstitiallighter fluid (liquid or gas) which may interact with theparticles to reduce the intensity of their interactions andhence boost the likelihood of propagation. Landslides,
avalanches (of rock, snow, or water), debris flows, andvolcanic events like pyroclastic flows and debris avalanches
are all examples of these types of granular flows. These
kinds of disastrous events are also witnessed underwater,such as submarine landslides, which can cause tsunamis,
damage underwater infrastructure, and even cause coastal
geomorphological changes [1-2]. Even though these natural
disasters got a lot of attention from scientists, they are still
hard to understand on a physical level [3-4]. The predictionof their final spread distance remains a top priority among
the numerous challenges induced by these flows, largely
because of the obvious concern caused by their destructive
power. Interestingly, these types of flows can travel a
distance that is several times larger than the height of thesource topography [5]. The ratio between the vertical fallheight and the horizontal spread distance is known as theangle of friction (𝛼𝑓 ) [6-7]. For loose granular material, theangle of friction is generally equal to the angle of repose.
However, if the material is compacted this relationship is nolonger valid.
As documented by several field observations, granulardebris flows include a broad range of particle sizes, fromboulders and gravel to silt and clay. For debris flow, themean particle sizes (𝑑50 ) are in the range of 2 to 200 mm
with a typical uniformity coefficient (𝐶𝑢 = 𝑑60 /𝑑10 ) in therange of 100 to 1000 [8-9]. Particle size distribution ofgranular materials along with their two parameters
uniformity coefficient 𝐶𝑢 and sorting coefficient ( 𝑆𝑐 =√𝑑75 /𝑑25 ), are often used to represent the gradation of
those material samples [10-11]. Dry granular sand with
𝐶𝑢 > 6.0 is generally referred to as a well-graded or nonuniform, while 𝐶𝑢 < 4.0 is characterized as a poorly gradedor uniformly graded sample. According to Trask [11], thedeposit is well-sorted if 𝑆𝑐 < 2.0, poorly sorted if 𝑆𝑐 > 4.5,and normally sorted if 2.0 ≤ 𝑆𝑐 ≤ 4.5. Different variables
influence the physical properties of these granular materials,
such as material composition, particle size distribution,
particle shape, mass density, and other properties [12, 13,14]. It is very difficult to determine the physical properties
of such granular materials. Conversely, there are implicit
links between particle size distribution and the physicalproperties of granular material [15]. Understanding thephysical behavior of granular debris flow requires finding
these implicit relationships. Few studies explicitly studied
the effect of mean particle size (𝑑50 ) and sorting coefficient(𝑆𝑐 ) on the flow behavior of granular material [8]. However,
the effect of 𝑑50 and 𝑆𝑐 on the final spread distance (𝐷𝑓 ) andangle of friction (𝛼𝑓 ) of such flows in water has received
mere attention. In this study, a mini conical-shaped mould
was used to understand the effect of 𝑑50 and 𝑆𝑐 on thephysical properties of various granular material samples
both in air and in water.

* Corresponding author: litanwre@gmail.com© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 01011 (2023)
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all three layers. Then, at a suitable speed, vertically remove
the mould and allow the sample to spread. The lifting speedof the mould may influence the slump-flow test results. Asa result, in this investigation, the lifting velocity of themould was maintained as slow and steady as possible foreach experiment. The human hand lifting speed of themould is often substantially less than 1 m/s, and lifting
speeds below 10 m/s had no discernible effect on the final
slump-flow results [18]. Figure 3 displays a schematic
illustration of the slump test procedure. For various material
samples, two primary variables are measured by using alaser distance meter, the final height of the deposit and thefinal spread distance as shown in Fig. 3c. The spread
distance of the deposit is measured in two perpendicular
directions, and the final spread distance ( 𝐷𝑓 ) for eachsample is given as the average of the two measurements.
Similarly, the average of three measurements for height wasused to get the final height 𝐻𝑓 . The dimensionless form of
the final spread distance was written as 𝐷𝑓∗ = 𝐷𝑓 /𝐷0 , where
𝐷0 is the bottom diameter of the initial sample ( i.e. 100 mm
in this study).

2 Materials and experimental procedure
2.1 Granular material samples
This investigation presents four different samples of
granular materials, and their particle size distribution isshown in Fig. 1. To evaluate the particle size distribution
and other parameters of each material sample, 900 grams ofmaterial with a particle density of 2.65 g/cm3 were used.
Table 1 displays the mean particle size 𝑑50 , uniformity
coefficient 𝐶𝒖 , and sorting coefficient 𝑆𝑐 for each material
sample. Samples 2 and 3 have 𝑆𝑐 < 2.0, indicating wellsorted samples, while samples 1 and 4 are normally sorted(2.0 < 𝑆𝑐 < 4.5). In other words, samples 1 and 4 are wellgraded or non-uniform (𝐶𝒖 > 6.0), while samples 2 and 3
are poorly graded or uniform (𝐶𝒖 < 4.0). The Corey shapefactor (SF) of 15 randomly chosen particles from eachsample was measured using a digital caliper, and theiraverage SF varied from 0.40 to 0.62. (Table 1).

Fig. 1. Particle size distribution of the tested samples
Table 1. Material properties of the tested samples. The unitof different particle sizes are in 'mm'

Sample

SF

𝑑10

𝑑25

𝑑50

𝑑60

𝑑75

𝐶𝑢𝑆𝑐

12
34

0.51
0.40
0.62
0.43

0.052
0.238
0.430
0.026

0.14
0.30
0.46
0.07

0.31
0.40
0.51
0.26

0.38
0.46
0.53
0.34

0.59
0.61
0.56
0.497.34
1.95
1.23
12.93

2.06
1.44
1.10
2.76

Fig. 2. Experimental setup of the slump test

2.2 Slump test procedure in airFig. 3. Schematic of the slump test procedure

Several researchers employed the slump test to evaluate
concrete flow ability and consistency. As described by Janet al. [16] and Jan and Dey [17], a downscaled conicalshaped mould was employed in this study for conducting
the slump test. The top inner diameter of the mould is 𝑑0 =50 mm, the bottom inner diameter is 𝐷0 = 100 mm, andthe height is 𝐻0 = 150 mm (Fig. 3a). A rectangular watertank of 60 cm long, 60 cm wide, and 40 cm in height wasconstructed (Fig. 2). Perspex glass with a thickness of 0.5
cm was used to construct the water tank. One person holds
the slump mould in the middle of the horizontal plane of theempty tank while another pours the material sample into themould. The sample material is poured in three layers into
the mould, then tamped 25 times with a steel rod to insurethat as little segregation as possible occurred during sample
preparation. The ends of the steel rod are rounded, andtamping was performed using the rod uniformly throughout

2.3 Slump test procedure in water
After carefully positioning the mould in the middle of thebottom plane of the empty water tank and filling it with thesample to be tested, the water tank is filled with water to adepth of 30 cm, which is twice the height of the slump
mould. To prevent causing turbulence or waves in the tank,the slump mould was lifted very gently and slowly. Wait fora considerable amount of time (roughly 2 to 3 mins) to allow
any suspended materials to settle. The final height (𝐻𝑓 ) andthe spread distance (𝐷𝑓 ) was measured by moving a ruler
along the scaffold (Note: underwater, a ruler is employed
instead of a laser distance meter since the laser distancemeter used in this investigation is not suitable to be used
underwater). Similar to the measurements in air, the final
spread distance is the average of two perpendicular readings
and the final height is the average of three readings [16].

2E3S Web of Conferences 415, 01011 (2023)
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3.2 Influence of mean particle size on final spread
distance and angle of friction

3. Results and discussions
3.1 Final deposit profiles

The influence of mean particle size 𝑑50 on thedimensionless final spread distance 𝐷𝑓∗ is shown in Fig. 7a.
Based on the results of the present study, the spread distance
reduces as the 𝑑50 of the samples increases, i.e. material
samples with smaller 𝑑50 have a larger spread distance andvice versa (Fig. 7a). Results obtained in water revealed thatthe spread distance in water seems to be influenced by thewater environment and is somewhat shorter than that in air(Fig. 7a). In other words, granular material sample with thesame 𝑑50 travels farther in air than in water. On the otherhand, the 𝑑50 has a significant impact on the angle offriction of granular material samples. A sample with asmaller 𝑑50 yields a gentler angle of friction, while a sample
with a larger 𝑑50 produces a steeper angle of friction (Fig.
7b). Comparing the results in air to those in water, the angleof friction underwater is somewhat found to be larger.

Figure 4 represents the final profiles of deposits for various
material samples and their two parameters, final height 𝐻𝑓and final spread distance 𝐷𝑓 are measured. It can beobserved from Fig. 4 that sample with a larger 𝑑50 produces
a lower spread and greater height of the final deposits andvice-versa. Similar behavior was also observed for all thematerial samples when the slump test was conducted inwater. However, the final height and spread distance inwater for a given 𝑑50 was found to be slightly smaller thanthat of in air. A comparison of the final deposit profile for𝑑50 = 0.51 in both air and water is shown in Fig. 5.

Fig. 4. Final shape profiles of the various material samples in air(a)(b)Fig. 7. Effect of mean particle size 𝑑50 on the (a) spread distanceand (b) angle of friction

Fig. 5. Final shape profiles of material samples with the same
𝑑50 = 0.51 mm in air and water

3.3 Influence of sorting coefficient on the final
spread distance and angle of friction

Based on the measured 𝐻𝑓 and 𝐷𝑓 , the angle of friction ofeach material sample was determined and is defined in Eq.
1.

Figure 8a&b shows the influence of the sorting coefficienton the final spread distance and angle of friction. In general,lower spread distance and larger angle of friction can beobserved for a well-sorted sample or a sample with a low
sorting coefficient (i.e. 𝑆𝑐 < 2.0). For the present study,
normally sorted samples (i.e. samples 2 and 3) show larger
spread distances and smaller angle of friction. Figure 8a&b
also reveals that for the same sorting coefficient, granular
flows in air have a larger spread distance than in water,whereas the angle of friction in air is lower than in water.

𝛼𝑓 = 𝑡𝑎𝑛−1 (2𝐻𝑓𝐷𝑓)(1)

Using this method (Eq. 1), the angle of friction is the baseangle of an idealized cone produced by linking the top andbottom points of the deposit body as shown in Fig. 6.
Previously Dong et al. [19] have used this method todetermine the angle of friction. In the above Eq. 1, the unitof 𝛼𝑓 is in radian.

(a)Fig. 6. Depiction of the angle of friction for the final deposit(b)Fig. 8. Effect of sorting coefficient 𝑆𝑐 on the (a) spread distance and (b)angle of friction

3

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6.

As seen in Figs. 7 and 8, the final spread distance and angleof friction vary in air and water. The following points mayhelp to explain these differences:(i) The granular flows in air have a longer spread distancethan that of corresponding flows in water due to a
reduction in effective gravity in the water environment[20].
(ii) According to Francesca et al. [21], due to the capillaryaction of water, negative excess pore pressure builds up
in water. This has a direct impact on how grains interact
in granular flow, which may significantly reduce
granular flow mobility in water.

7.
8.
9.
10.
11.
12.

Figure 7b illustrates that the angle of friction increases as
the 𝑑50 increases, which contradicts the results of Jan [22]and Grasselli and Herrmann [23]. Their findings forhomogenous glass sphere mixtures show that the angle offriction decreases with the 𝑑50 . These variations might becaused by differences in sediment shape factors (Table 1).

13.
14.
15.
16.

4 Conclusions
The following conclusions may be inferred from the present
experimental results and analyses:(i) A sample of granular material with a smaller mean
particle size (𝑑50 ) travels farther than one with a larger𝑑50 .
(ii) The angle of friction of a sample with a lower 𝑑50 issmaller than the sample with a higher 𝑑50 .
(iii) The spread distance is shorter for a sample with a low
sorting coefficient (𝑆𝑐 ), but the angle of friction is higher.
(iv) The spread distance of granular material samples inwater is slightly shorter than that in air. While the angleof friction in water is slightly higher than that in air.

17.
18.
19.
20.
21.

These results demonstrated that thorough laboratory studies
may provide insight into the physical properties of granulardebris flow on land as well as underwater. Further
investigations are required to understand how the particle
size distribution and sorting coefficient influence the final
spread distance and angle of friction when both 𝑑50 and 𝑆𝑐
vary individually. In addition, it is recommended that theinfluence of bottom roughness, interstitial fluid density, andparticle shape on the physical parameters of such flows beinvestigated.

22.
23.

This experimental work was conducted in the HydraulicLaboratory of the National Cheng Kung University, Taiwan, andfinancially supported by the National Science and Technology
Council, Taiwan (NSTC–110–2221–E–006–062).

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