京 都 大 学 防 災 研 究 所 年 報 第 50 号 B 平 成 19 年 4 月
Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 50 B, 2007

Classification of Grain Size Distribution Curves of Bed Material and the Porosity
Muhammad SULAIMAN*, Daizo TSUTSUMI, Masaharu FUJITA
and Kunihiko HAYASHI***Graduate School of Engineering, Kyoto University**Faculty of Engineering, Kyoto University
SynopsisAmong the qualitative features of bed material, the grain size distribution and theporosity are very important properties governing a habitat condition of aquatic living things.
Two topics will be considered in this paper. The first is the identification and classification ofgrain size distribution curves and the second is measurement of the porosity of sedimentmixtures and bed material. Grain size distribution of actual sediment mixture can be roughlyclassified into three types of distribution, namely, log-normal distribution, Talbot distribution
and bimodal distribution, based on the mode of density distribution and indices β and γ. The
porosity could be reasonably estimated by measuring the in-situ volume of sediment sample.
Keywords: classification, grain size distribution, porosity, sediment mixture, bed material

1. Introduction
Assessing the change in void structure of riverbed
material is very important for an ecological issue inrivers. The effects of porosity changes fromsedimentation on the riverbed environment have been
widely investigated (Milhous, 1982; ASCE, 1992).
Particularly, many ecologists are interested in thevoid structure of the bed material (Gayraud andPhilippe, 2003). The previous bed variation models
are available for the analysis of bed variation and thechange in grain size distribution. However, theycannot provide information on the change in porosity.
The porosity of bed material is usually assumed to bea constant. Fujita et al. (2005) have presented aframework of riverbed variation model to simulate
the change of porosity as well as bed variation. A
simple analytical model has been already presented
under this framework, for a sediment mixture ofparticles with two much different grain sizes.
However, it cannot be used for general grain size
distribution. The porosity of sediment mixtures
depends on the grain size distribution (Standish andBorger, 1979; Tsutsumi et al., 2006). If the porosity
is related to the grain size distribution, the simple
model could be improved in applying to generalcases.
Actual sediment mixtures have various types ofgrain size distribution. Therefore, it is necessary toobtain the porosity for each grain size distribution
one by one in calculation of bed variation. However,

it is not practical. It is better to install somerelationships between porosity and typical grain size
distribution in the bed variation model in advance.
For that modeling, classification and identification of
the grain size distribution type are necessary.
This study aims to develop a method forclassifying the type of grain size distribution curveand obtaining the porosity for the different type ofgrain size distribution. Two topics will be consideredin this paper. The first is the identification andclassification of grain size distribution curves and thesecond is measurement of the porosity of sedimentmixtures and bed material. Firstly, three types oftypical grain size distribution namely log-normal
distribution, Talbot distribution and bimodal
distribution were introduced. The grain size
distributions of sediment mixture in natural rivers
were classified into typical grain size distribution,and the parameters on those geometric properties
were found out. Then, a method for identifying andclassifying the type of grain size distribution waspresented. Secondly, a method for measuring theporosity of sediment mixture and bed material waspresented. A laboratory experiment and fieldobservation was conducted to measure the porosity ofthe sediment-mixtures with different type of grain
size distribution. The results of measured porosity
were presented together with relationship between
the porosity and the geometric parameter of grain
size distribution was obtained by means of a packing
model developed by Tsutsumi et al. (2006).

－ 615 －

2.

Classification of Grain Size Distribution
Curves

A grain size distribution is said to be bimodal if thedensity distribution p(d), displays two distinct peaks.
Each peak is a mode of a portion of the distribution.
When the geometric averages of grain size are dmgAand dmgB, the standard deviation are σLA and σLB, themixing ratio are pA and pB (=1-pA), the parameters
governing porosity are σLA ,σLB, dmgA /dmgB and pA.

2.1 Typical grain size distribution
Riverbed materials have a variety of different
characteristic size of bed surface sediment, but thegrain size distribution could be classified into some
types. In this study, the grain size distributions areroughly classified into three types of grain size
distribution, namely, log-normal distribution, Talbot
distribution and bimodal distribution. Typical of thegrain size distributions of sediment mixture areshown in Figure 1, where f is the percentage of thefiner grain size and p(=df/d(logd)) is the density
function of grain size.
The density function of log-normal grain size
distribution is as follows:⎡ (ln d − ln d mg )2 ⎤exp ⎢−⎥
22(σ L )
2π σ L⎢⎣⎥⎦1p(ln d ) =2.2 Data
Riverbed materials have a variety of different
characteristic size of bed surface sediment (Bunte
and Abt, 2001), but the grain size distribution could
be classified into some types. One of the most typicaldensity functions of grain size is a log-normal
distribution. The grain size distribution of bed
material in most sand-bed streams is unimodal andthat in many gravel-bed rivers is bimodal (Parker,
2004). Also in mountainous rivers, the surface bed
material has usually Talbot distribution of grain size
(Tatsuzawa et al., 1998).
The grain size distribution of natural riverbed
material and produced sediment were collected foranalysis of identification and classification of grain
size distribution. The samples were taken from Ai
River (Fujita, 2004), Hino River (MLIT, 2004),
Ohtaki River (Ashida and Fujita, 1987) and Fukadanibare slope. The grain size distributions and thosedensity distribution are shown in Figures 2 and 3.
Capital letter A, H, O and F denote the samples from
Ai River, Hino River, Ohtaki River and a Fukadanibare slope, respectively. The sampling points are
summarized in Table 1. The samples were classified
by the characteristics of sampling points as follows:a) Surface bed material (A-1, 5, H-1, 2, 3)b) Sub-surface bed material (A-2, 6, H-4, 5, 6)c) Sand bar (A-3)d) Sediment deposition in a sabo dam (A-4)e) Sediment deposition in a valley immediately
after Ontake Lanslide 1984 (O-1)
f) Sediment deposition in a reservoir (O-2, 3)g) Sediment produced at a bare slope (F-1, 2, 3)(1)

where dmg is the geometric average of grain size andσL is the standard deviation of lnd. Normalizing dwith dmg, σ L is only a parameter of the log-normal
distribution. The porosity of the mixture is, therefore,
dependent on σ L. For Talbot distribution, we
modified the original Talbot distribution function,
Eq.(2), with considering the minimum diameter ofthe grain size as shown in Eq.(3). The porosity of the
mixture is determined with a coefficient namely
Talbot number, nT, with nT > 1, and ratio of
maximum and minimum diameter, dmax/dmin.

⎛ d ⎞
⎟⎟
f (d ) = ⎜⎜⎝ d max ⎠n(2)⎛ log d − log d min ⎞⎟⎟f (d ) = ⎜⎜⎝ log d max − log d min ⎠nT

fnT > 1

(3)

f

d

f

d

p

p

log(d)(a) Log-normal typedplog(d)(b) Talbot typelog(d)(c) Bimodal typeFig.1 Typical of grain size distribution of sediment mixture and the density
function of grain size

－ 616 －

100

80
60
40
20

100

H-1
H-2
H-3
H-4
H-5
H-6

80
60
40

Percent finer (% )

A-1
A-2
A-3
A-4
A-5
A-6

Percent finer (% )Percent finer (% )

100

1

10
d (mm)

100

1000

60
40

0

0

0.1

80

20

20

0

O-1
O-2
O-3
F-1
F-2
F-3

0.1

1

a) Ai River10d (mm)

100

1000

0.001

b) Hino River

0.01

0.1

d (mm)

110100c）Ohtaki River and FukadaniFig. 2 Grain size distributions of bed material and produced sediment

p

p

2

2

1

O-1
O-2
O-3
F-1
F-2
F-3

2

H-1
H-2
H-3
H-4
H-5
H-6

p

A-1
A-2
A-3
A-4
A-5
A-6

3

1

1

0

0

0

-1

0

1

2

3

-1

0

1

log d

a) Ai River

2

log d

b) Hino River

3

-3

-2

-1

0

1

2

log d

c）Ohtaki River and FukadaniFig. 3 Density distributions of grain size distribution shown in Fig.2
2.3 Identification and classification
The grain size distributions of natural sedimentmixture can be identified and classified visuallybased on the shape of size distribution and density
distribution. The grain size distribution classified into
log-normal distribution if the trend of the size
distribution curves similar to log-normal curve andthe density distribution has a single peak. If thedensity distribution is skewed towards a high-end tailof distribution, the grain size distribution is classified
into Talbot distribution. If the density distribution has
two peaks, the grain size distribution classified into
bimodal distribution.
As shown in Figure 3, the shapes of density
distribution p are quite different from each other.
Therefore, the type of grain size distribution can be
identified if an index expressing the shape of density
distribution p found out. Figure 3 shows the numberof peak of density distribution for bimodal
distribution is two. It is easy to understand that the
number of peak, np, is an index for determine of
unimodal or bimodal distribution. A-2, A-4, H-4 andH-5 are therefore, identified as bimodal distribution.
In addition, the following two indices are taken:
β=log d max − log d 50 (4)log d max − log d peak ;γ=
log d max − log d minlog d max − log d min

where dmin is minimum size, d50 is 50% size, dmax is
maximum size, and dpeak is a diameter which give
maximum value of p. These indices designate therelative locations of d50 and dpeak between dmin anddmax. β and γ are 0.5 for ideal log-normal distribution
and 0.0 for ideal Talbot distribution. Actually, thecritical value of these indices should be determinedfor each type.
A type of the distribution can be determined by
the shape of size distribution, the shape of density
distribution, and values of β and γ . The values of βand γ for each grain size data are listed in Table 1.
Figure 4 shows the relation between β and γ. A-1,
A-5, A-6, H-6, F-1, F-2 and F-3 plotted with filled
circles are visually identified as Talbot distribution.
H-3 and O-1 plotted with triangles are visually
identified the distribution between Talbot andlog-normal. A-3, O-2, O-3 plotted with open circles
are visually identified as log-normal distribution. H-1
and H-2 plotted with cross are the distribution
between log-normal and anti-Talbot. Anti-Talbot
distribution is defined by Eq. (3) with value of
Talbot number, nT, less than 1 (nT < 1).
Based on the visual identification and the relation
between β and γ, the critical value of these indicesfor each type distribution can be determined. The
critical values of the indices were determined byadding and reducing the value of β and γ for
log-normal distribution (0.5) with certain value α.
According to the relation between β and γ as shownin Figure 4, the value of α=±0.2 is reasonable. Grainsize distributions are classified into Talbot type if
β≤0.3 and γ≤0.3, log-normal type if 0.3<β<0.7 and0.3<γ<0.7 and anti-Talbot type if β >0.7 and γ >0.7.

－ 617 －

Table 1 Parameters of actual grain size distribution
No.

d min

Sample sites

d 50
(mm)

d peak

d max

(mm)

(mm)

(mm)

β

γ

np

Type

A-1

Surface bed in upstream of Gokuraku Bridge in Ai River

0.740

149.23159.00381.00

0.14

0.15

1

T

A-2

Sub-surface bed in upstream of Gokuraku Bridge in Ai River

0.370

57.70

67.80

381.00

0.25

0.27

2

B

A-3

Sand bar in downsream of Gokuraku Bridge in Ai River

0.370

12.77

8.50

47.60

0.35

0.27

1

L

A-4

Deposit in Ai gawa sabo dam in Ai River

0.370

67.80

159.00750.00

0.20

0.32

2

B

A-5

Surface bed near Kurumatukuri Bridge in Ai river

2.500

409.49381.00750.00

0.00

0.11

1

T

A-6

Sub-surface bed in Kurumatukuri Bridge in Ai river

0.370

62.75

159.00381.00

0.13

0.26

1

T

H-1

Surface bed in the upstream of river mouth of Hino River

19.000

70.14

37.50

250.00

0.74

0.49

1

AT

H-2

Surface bed in Lower Hino River

19.000

94.57

37.50

400.00

0.78

0.47

1

AT

H-3

Surface bed in Middle Hino River

19.000191.18150.00400.00

0.32

0.24

1

T

H-4

Sub-surface bed in the upstream of river mouth of Hino River

0.100

5.70

0.85

250.00

0.73

0.48

2

B

H-5

Sub-surface bed in Lower Hino River

0.100

9.50

37.50

400.00

0.29

0.45

2

B

H-6

Sub-surface bed in Middle Hino River

0.100

45.00

250.00400.00

0.00

0.26

1

T

O-1

Deposit in Ohtaki River immediately after Ontake Landslide, 1984

0.001

0.44

1.00

25.00

0.32

0.40

1

T

O-2

Deposit of wash load in Makio Reservoir

0.001

0.03

0.03

0.25

0.42

0.38

1

L

O-3

Deposit of bed material load in Makio Reservoir

0.050

1.45

1.00

25.00

0.52

0.46

1

L

F-1

Sediment produced at Fukadani bare slope on May 28,2002

0.020

7.08

40.00

100.00

0.00

0.31

1

T

F-2

Sediment produced at Fukadani bare slope on July 1,2002

0.020

9.29

40.00

100.00

0.00

0.28

1

T

F-3

Sediment produced at Fukadani bare slope on November 12,2002

0.020

25.49

40.00

100.00

0.00

0.16

1

T

L: Log-normal distribution ; T: Talbot distribution; B: Bimodal distribution；AT: Anti-Talbot distribution
1.0

Anti-Talbot

0.8
Lognormal

β

0.6
0.4
Talbot0.2

TalbotLognormal
Talbot--Log-normal
Anti Talbot--Log-normal

0.0
0.0

0.2

0.4

γ

0.6

0.8

1.0

Fig.4 Relation between β and γ(after Sulaiman et al., 2007)
3. Measurement of Porosity
3.1 Measurement method
Porosity is the most widely used parameter forassess the interstitial space both in sediments and insoils. The porosity is normally defined as the ratio of
the pore volume to the total volume of a given
sample. The porosity could have been calculated
from the measured sediment volume base on a water
displacement process. A schematic diagram
explaining the measurement method of the porosity isshown in Figure 5. The method use to determine theporosity is a simple method. The technique is tomeasure the in situ volume of sediment-mixtures
sample by measuring the volume of a ring over the
sediment-mixtures and then repeated the volume
measurement after the sample is obtained fromwithin the ring. The difference in the volumes is thetotal volume of the sample.
A PVC (Polyvinyl Chloride) ring with 30 cm of
diameter and 5 cm height was used. The equipments
needed to measure the porosity are: water levelmeasure, point gauge, vinyl sheet, 2000 cc cylinder,

and vinyl bag. All the equipment can be carried in.
The process for determining the porosity is asfollows:
1. Position and set the PVC ring stable and inhorizontal position by using the water levelmeasure, on the sediment sample or bed material
where the porosity is to be measured.
2. Determine the volume of the ring below somedatum (V1); place the tripod with adjustable point
gauge above the ring to control the water level.
Place plastic sheet in the ring and fill the water,
measuring the volume of the water placed in thering. The filling of water was stopped when thewater is up to the point gauge. Make careful noteof the volume of the water placed in the ring (V1).
Remove the water from the ring being very
careful not to disturb the ring.
3. Remove the surface sediment sample or surface
bed material layer (armor layer) by tacking
volumetric sample within the ring andcontinuing to be very careful not to disturb thering. The required sample size is not welldefined. In this study, reasonable results havebeen obtained when the sample size is between
3-5 kg. In the case of sampling riverbed material,
the thickness of the armor layer is described as
extending from the bed-surface plane down tothe bottom side of the largest particle size (dmax)
or a frequently occurring large surface particle
size (ddom).
4. Retain the material removed for sieve analysis
and measure the volume of the sediment. The
hole should be as smooth sided as possible.
5. Determine the volume of the hole dug to remove
the sediment or bed-material sample; place theplastic sheet on the surface and fill the water into
the hole and ring to the same level as the first
volume measurement (controlled by the point－ 618 －

5 cm

Point gauge

PVC ring (diam. 30 cm)

Water

V1

Point gauge

Water

V2

Vt = V2- V1
Porosity

dry sediment

Vw

Vs+w

V −V
p= t sVt

Size distribution
measurement(sieving test)

Vs= Vs+w- Vw

Fig.5 Measurement of porosity

6.
7.

8.

gauge). The volume of the water must be
determined during the process of filling (V2).
Calculate the volume of the hole (Vt) by
subtracting the ring volume (V1) from the holeplus ring volume (V2).
Dry and measure the weight of the sample. The
specific weight is calculated from the weight andvolume. Sieve the sample and determine the size
distribution curve.
Measure the volume of the sediment (Vs); thesediment or bed-material sample and water werefilled into a cylindrical vessel carefully up to aplace marked on the inside of cylindrical vessel.
Remove the air content in the bed material as
much as possible during filling the sample byshaking the cylindrical vessel. Note the total
volume of sediment and water (Vs+w). Make
careful note of the volume of the water placed in
the cylinder (Vw). The volume of the sediment(Vs) is calculated by subtracting the water
volume (Vw) from the total volume of sedimentand water (Vs+w)

V − Vs
9. Calculate the porosity: p = t
Vt

3.2 Laboratory experiment and field observation
A laboratory experiment was conducted tomeasure the porosity of the sediment-mixtures withdifferent type of grain size distribution. Ten different
kinds of grain size distribution were prepared; consistof five lognormal distributions with different
standard deviation (i.e., 0.02, 0.253, 0.29, 0.303, and1.6), and five bimodal distributions. The
characteristic of sediment for bimodal distribution isshown in Table 2. Five different fine proportions pA(i.e., 0.1, 0.2, 0.3, 0.4, and 0.5) were prepared. The
grain size distribution of the samples for lognormal
distribution and bimodal distribution are shown in
Figure 6 and Figure 7 respectively. The porosities
were measured five times for each grain size

distribution.
A field observation was conducted to measure
the porosity of the armor layer and sub armor layer ina dry part of the streambed. The location of the fieldobservation is in the bar of Uji River located in frontof Ujigawa Open Laboratory. The grain size
distribution of armor layer and sub armor layer isshown in Figure 8. Base on the shape of grain size
distribution curve, the distributions were classified
into Talbot distribution. By using fitting curve with
Eq.(3), the Talbot number of the armor layer sample
and the sub armor layer is 5.0 and 2.5 respectively.
3.3 Measurement results
The measured porosities as related to the grain
size parameter for each type distribution arepresented together with relationship between theporosity and the geometric parameter of grain size
distribution was obtained by means of a packing
model developed by Tsutsumi et al. (2006).
(1) Log-normal distribution
The mean porosity of five repetitions of themeasured porosity for five different grain size
distributions showed in Figure 6 are shown in
Figure 9. The relationship between the standard
deviation of the lognormal distribution, lnσ, and thesimulated porosity presented by Tsutsumi et al.
(2006) also shown in Figure 9 together withmeasurement results. The error bars indicate theranges between maximum and minimum values offive repetitions. The porosity varied with the grain
size distribution. For the relatively uniformthe measured porosity
distribution (lnσ=0.02),
widely ranged from 0.282 to 0.376 with the meanporosity is 0.321. The mean value differed from thesimulation result. The widely ranging measured
porosity for this distribution arises from thedifference in the particle packing and the shape ofparticle.

－ 619 －

Percent finer (%)

100

The mean value of the measured porosity
decreased as the standard deviation lnσ increased
from 0.253 to 1.6. The mean measured porosity
differed from the simulation result; the measured
porosities are greater than simulations results. The
discrepancy may be due to differences in the shape ofparticle. In the measurement, the particles were used
is non-spherical particle, while in the simulation theparticles were assumed as sphere.

L1

σ=0.0280

L2σ=0.253L360

σ=0.29L440

σ=0.303
L5

σ=1.6

20
0
0.01

0.1

1

10

100

of

lognormald (mm)

Fig. 6 Grain size
distribution sample

distribution

Percent finer (%)

100
pA=0.180

pA=0.260

pA=0.340

pA=0.420

pA=0.5

0
0.1

1

10

(2) Bimodal distribution
Bimodal distribution generally ranges widely. In
this study the artificial bimodal distributions withnarrow distribution were used. The characteristic ofmaterials are shown in Table 2. The characteristic issimilar with the characteristic of materials were used
for particle packing simulation by Sulaiman et al.,(2007). Porosities for seven different fine proportionspA (i.e., 0.0, 0.1, 0.2, 0.3, 0.4, 0.5 and 1.0) were
measured. Relationship between fine proportion pA(by volume) of mixture and the mean porosity of thefive measured porosity for two fraction mixture areshown in Figure 10. The porosity of bimodal
distribution depends on the percentage of eachfraction in the mixture and a porosity minimum isobserved.

d (mm)

Table 2 Characteristic of sediment for bimodal
distribution

Fig. 7 Grain size distribution of bimodal distribution
sampleFraction

σ

dmin
(mm)

d50
(mm)

dmax
(mm)

A

0.2

0.5

1.0

2.0

B

0.2

2.0

4.0

8.0

Percent finer (%)

100
sub-armor layer

80nT=2.5armor layer

60

nT=5.0

40
20
0
0.01

0.1

1

10

100

d (mm)

Fig. 8 Grain size distribution of the armor layer and
sub armor layer of Uji River bar

Porosity

0.4

0.3

0.2
Measured
Simulated (Tsutsumi et al., 2006)

0.1
-0.1

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Standard deviation σ L

Fig. 9 Comparison of the porosity, between themeasured and simulated results for lognormal
distribution with different standard deviation

The results were compared with the mean porosityof the five repetitions of the simulated porosity for
two fraction mixture by using particle packing model
presented by Sulaiman et al. (2007). Interestingly, thechange of porosity is similar and a porosity minimum
is observed. The discrepancy between the measured
and simulated porosity may be due to differences in
the uniformity of the mixture of sediment sample andthe packing of particle. In the measurement, theparticles were used is non-spherical particle, while inthe simulation the particles were assumed as sphere.
(3) Talbot distribution
The mean porosity of five repetitions of themeasured porosity for two different grain size
distributions showed in Figure 8 are shown in
Figure 11. The relationship between the Talbot
number, nT, and the simulated porosity presented by
Sulaiman et al., (2007) also shown in Figure 11
together with the measurement results. For thesimulation results with dmax/dmin=10, the porosity
increased from 0.241 to 0.314 when the Talbot
number, nT, increased from 2 to 8. The porosity
increased from 0.173 to 0.273 for dmax/dmin=100 when

－ 620 －

the Talbot number, nT , increased from 4 to 12. The
porosity of Talbot distributions increased with anincreasing of the Talbot number nT. Smaller ratio of
dmax/dmin gives the higher value of porosity.

Porosity

0.4
0.3
0.2
measuredsimulated (Sulaiman et al., 2007)

0.1
0

0.2

0.4

0.6

0.8

1

Fine proportion by volume

Fig. 10 Comparison of the porosity, between themeasured and simulated results for bimodal
distribution with different fine proportion.

indices β and γ. To determine the exact
distribution type, it’s necessary to find out
another index.
2) The porosity of sediment mixtures and bed
material could be reasonably estimated bymeasuring the in-situ volume of sediment sample.
3) Relationship between the grain size distribution
and the porosity can be determined by using thegeometric properties of grain size distribution.
The porosity of log-normal distributions
decreased with an increasing standard deviation.
The porosity of Talbot distributions increased
with an increasing of the Talbot number nT andsmaller ratio of dmax/dmin gives the higher value ofporosity. The porosity of bimodal distribution
depends on the percentage of each fraction in the
mixture. The porosity of armor layer is higher
than the porosity of sub-armor layer.
4) A method use to measure the porosity is a simple
method and there is a need to improve themethod for better accuracy.

0.4

References

Porosity

0.3
0.2
0.1

simulated : dmax/dmin=10 (Sulaiman et.al., 2007)
simulated: dmax/dmin=100 (Sulaiman, et.al., 2007)
measured : dmax/dmin=181.2

0.0
0

2

4

6
nT

8

10

12

Fig. 11 Comparison of the porosity, between themeasurement and simulated results for Talbot
distribution with different Talbot number
The measured porosity of armor layer ranged
from 0.224 to 0.336 with the mean value is 0.265.
The measured porosity of sub-armor layer is smaller
than surface bed material; ranged from 0.168 to 0.230
with mean value is 0.195. The porosity of sub-armor
layer is smaller than armor layer because thesub-armor layer contains much more fine sedimentthan armor layer. The change of the porosity issimilar with the simulation results, where the porosity
increased with an increasing Talbot number.
4. Conclusions
A method for identifying the type of grain size
distribution curve and obtaining the porosity for thedifferent type of grain size distribution weredeveloped. The results are as follows:
1) Grain size distribution of actual sediment mixture
can be roughly classified into three types of
distribution, namely, log-normal distribution,
Talbot distribution and bimodal distribution,
based on the mode of density distribution and

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河床材料の粒度分布の分類と空隙率

Muhammad SULAIMAN*・堤大三・藤田正治・林邦彦***京都大学大学院工学研究科**京都大学工学部

要旨

河床材料の粒度分布と空隙率は，河川の水生生物の生息環境として非常に重要な要素である。本稿では，それらに関する事項のうち2点に関して検討した内容について発表する。ひとつは，河床材料の粒度分布曲線を特定し，分類する手法に関して，もうひとつは，自然河川の河床材料や人為的に調整した混合土砂材料の空隙率の測定方法に関するものである。河床材料の粒度分布は，その確率密度分布の関数指標βとγに基づき，対数正規分布，タルボット型分布，二山型分布の大まかに3種類の分布に分類することができる。一方，河床材料の空隙率は，砂礫体積の現位置測定によって評価することが可能である。

キーワード：分類，粒度分布，空隙率，混合砂礫，河床材料－ 622 －