Sediment transport and sediment properties
7.2 PHYSICAL PROPERTIES OF SEDIMENTS .1 Introduction
7.2 Physical properties of sediments 155
Notes
1. Both ripples and dunes are observed with wind-blown sand and in open channel flow (Fig. 7.2a and b).
2. Note that, in alluvial rivers, dunes form with subcritical flow conditions only. Antidunes are associ- ated with supercritical flow while standing waves are characteristics of near-critical flow conditions.
3. The transition between dune and standing-wave bed forms occurs with a flat bed. The flat bed is an unstable bed pattern, often observed at Froude numbers slighlty below unity: e.g. Fr = 0.77 (Kennedy, 1963), 0.83 (Laursen, 1958) and 0.57-1.05 (Mien and Rastan, 1998).
Discussion
Ripples are associated with the presence of a laminar boundary layer. Their size is independent of the flow depth d. Usually their characteristic dimensions (length / and height h) satisfy / « lOOOc? and h < 100 J.
Dunes are associated with a turbulent boundary layer. In rivers, their size is about proportional to the flow depth (see also Table 12.3). In open channels, dunes take place in subcritical flow.
With standing-wave and antidune bed forms, the fi*ee-surface profile is in phase with the bed form profile. In natural streams, antidunes and standing waves are seldom seen because the bed forms are not often preserved during the receding stages of a flood. Kennedy (1963) investigated standing- wave bed forms in laboratory while Alexander and Fielding (1997) presented superb photographs of gravel antidunes.
7.2 PHYSICAL PROPERTIES OF SEDIMENTS
Table 7.2 Sediment size classification Class name
(1) Clay Silt Sand Gravel Cobble Boulder
Size range (mm) (2)
t/s< 0.002 to 0.004 mm 0.002 to 0.004 < ^s < 0.06 mm 0.06 <fi?s< 2.0 mm
2.0 <fi?s< 64 mm 64 < ^ s < 256mm 256 < d.
Phi-scale (<^) (3)
+ 8to+9<</>
+ 4 < < ^ < +8to +9 - 1 < < ^ < +4 - 6 < ( / > < - 1 - 8 < < ^ < - 6
</><-8
Remarks (4)
Silica
Rock fragments Original rocks Original rocks
The most important property of a sediment particle is its characteristic size. It is termed the diameter or sediment size, and denoted d^. In practice, natural sediment particles are not spher- ical but exhibit irregular shapes. Several definitions of sediment size are available:
• the sieve diameter,
• the sedimentation diameter,
• the nominal diameter.
The sieve diameter is the size of particle which passes through a square mesh sieve of given size but not through the next smallest size sieve: e.g. 1 mm < d^< 2 mm.
The sedimentation diameter is the size of a quartz sphere that settles down (in the same fluid) with the same settling velocity as the real sediment particle. The nominal diameter is the size of the sphere of same density and same mass as the actual particle.
The sediment size may also be expressed as a fimction of the sedimentological size parameter </>
{ox Phi-scale) defined as:
d^ = T^ (7.2a) or
</> =
ln(2) (7.2b)
where d^ is in mm.
A typical sediment size classification is shown in Table 7.2.
Notes
1. Large particles are harder to move than small ones.
2. Air can move sand (e.g. sand dunes formed by wind action). Water can move sand, gravel, boulders or breakwater armour blocks (weighting several tonnes).
3. The sedimentation diameter is also called the standard fall diameter.
7.2.3 Properties of sediment mixture The density of a dry sediment mixture equals:
(Psed)dry = ( 1 " ^ ^ ) P s
where Po is the porosity factor.
(7.3)
7.2 Physical properties of sediments 157 The density of wet sediment is:
(Psed)wet = Pop + (1 - Po)p, (7.4) The porosity factor ranges basically from 0.26 to 0.48. In practice, Po is typically about
0.36-0.40.
Notes
1. The density of sediments may be expressed also as a function of the void ratio: i.e. the ratio of volume of voids (or pores) to volume of solids. The void ratio is related to the porosity as:
Void ratio = Po/(l - Po)
2. Another characteristic of a porous medium is the permeability. For a one-dimensional flow through the pores of the sediment bed, the velocity of seepage is given by the Darcy law:
dx
where K is the hydraulic conductivity (or coefficient of permeability, in m/s) and H is the piezo- metric head (in m). The hydraulic conductivity not only depends on the permeability of the soil but also on the properties of the fluid and dimensional analysis yields (Raudkivi and Callander,
1976: p. 15):
where k is the permeability (in m^), p is the fluid density, g is the gravity constant and /z, is the fluid dynamic viscosity. Typical values of the hydraulic conductivity are (Raudkivi and Callander, 1976: p. 19):
Soil type: Fine sand Silty sand Silt K (m/s): 5 X IQ-^ to 1 X IQ-^ 2 X 10"^ to 1 X IQ-^ 5 X lO'^ to 1 X 10"^
3. Discussion: conversion between parts per million (ppm) and kilograms per cubic metre (kg/m^).
For suspended sediment, the sediment concentration may be expressed in kg/m^ and it is calcu- lated as the ratio of dry sediment mass to volume of water-sediment mixture. It can be expressed also as a volume concentration (dimensionless). Another unit, ppm, is sometimes used. It is defined as the ratio of the weight of sediment to the weight of the water-sediment mixture times one million.
The conversion relationships are:
Mass concentration = pjC^
Concentration in ppm by weight = 1 X I O S Q
1 + (s - \)C, where C^ is the volumetric sediment concentration and s = pjp.
Application
Calculate the dry and wet densities of a sand mixture with a 38% porosity.
Solution Assuming a mated using
quartz sand (p^
equations (7.3) j
(P
= 2650 m^/s), the dry and wet densities of sediment mixture md (7.4):
(Psed)dry ~ (^ ~
sed)wet = Pop +
- Po)p, = 1643 kg/m^
(1 - Po)p, = 2022 kg/m^
are esti-
7.2.4 Particle size distribution
Natural sediments are mixtures of many different particle sizes and shapes. The particle size distribution is usually represented by a plot of the weight percentage of total sample, which is smaller than a given size plotted as a function of the particle size. A cumulative curve fitted to data points is shown in Fig. 7.3.
The characteristic sediment size d^Q is defined as the size for which 50% by weight of the material is finer. Similarly the characteristic sizes diQ, djs and dgo are values of grain sizes for which 10%, 75% and 90% of the material weight is finer, respectively.
d^o is commonly used as the characteristic grain size and the range of particle size is often expressed in terms of a sorting coefficient S:
(7.5)
Another descriptor is the geometric standard deviation based upon a log-normal distribution of grain sizes a^:
(7.6) Small values of 5 and a^ imply a nearly uniform sediment size distribution. A large value of iS means a broad sediment size distribution.
0.01 0.1
ds (mm)
10 1.00
0.90 0.80 0.70 0.60
0.50 j 0.40 j 0.30 j 0.20 1 0.10 0.00
% sample % passing
_ ^^^m^^ip^^i .,. I ^
— I — I — ^ - i - ' ^ I C ^ -
4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 - 0 . 5 - 1 - 1 . 5
1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 1-0.10 0.00 2 - 2 . 5 (f)
Fig. 7.3 Typical particle size distribution curve: (a) percentage sampling as a function of sedimentological size parameter <^
(linear scale) and (b) cumulative percentage passing as a function of the particle size d^ in mm (semi-logarithmic scale).
7.3 Particle fall velocity 159
Notes
1. The sediment size d^o is called the median grain size.
2. Other definitions may be used to characterize the range of particles sizes. For example:
Gradation coefficient = - [ ^ + ^
2 I ^50 ^16 J (Mien, 1995) 3. The size distribution may be recorded using a settling tube (see next sections).
Comments
The size distribution of cohesive sediments (e.g clay and silt) may vary with the environmental conditions to which the sediments have been subjected and also the procedures which are used to determine their size distribution. In the following, we shall primarily consider non-cohesive sediments.
7.3 PARTICLE FALL VELOCITY