Erodibility of Bank Materials

CONCLUSIONS AND RECOMMENDATIONS 9.1 A Brief Review of the Work Done

2.2 Erodibility of Bank Materials

The erodibility of the bank soil materials is the important factor for fluvial erosion. This erodibility is directly related with the critical shear stress of soil. Critical shear stress is the shear stress developed due to flowing water over a soil surface at the initiation of the scour. Several investigations were carried out for determining the critical shear stress of different soil materials. Some important investigations and their methods are discussed below.

Shields (1936) developed a diagram based on particle size to estimate the critical shear stress of the non-cohesive soils assuming no interaction between the sediment

particles. The study was carried out in uniform non-cohesive particle for which fluvial entrainment is a function of hydraulic lift and drag forces.

Smerdon and Beasley (1961) carried out the study in laboratory flume for determining the relationship of the critical shear stress with the basic soil properties.

Eleven cohesive bank soils from the Missouri river were investigated in that study. The collected soil samples were placed in the flume without compaction. The soils were tested under increasing flow rates and the shear stress corresponding to the bed failure was considered as the critical shear stress. Different empirical relationships were developed and are shown through the following equations:

0.16 ( )0.84

c Iw

τ = × (2.1) 10.2 ( ) 0.63

c Dr

τ = × ⁻ (2.2)

28.1 50

3.54 10 ^D

τc = × ⁻ (2.3)

0.0182

0.493 10 ^Pc

τc = × (2.4) where, τ^c critical shear stress (Pa), I_w plasticity index, D_rthe dispersion ratio, D₅₀mean particle size (m), Pc the percent clay by weight (%). Clark and Wynn (2007) suggested that the relations with I_w and D_r are most relevant as they directly relate with cohesive properties of soil.

Neill (1967) documented the experimental data on the incipient motion for six sizes of graded gravels, two sizes of uniform glass balls, and cellulose acetate balls, diameters of which ranges between 6 and 30 mm. for a wide channel. The flow was uniform over the flat flume bed. After analyzing the experimental data he presented an equation with mean velocity, grain size, specific gravity and flow depth:

2 0.20

' ^mc 2.50 ^g

s g

V D

D d

ρ γ

 −

=  

  (2.5) where, Vmc the mean velocity component for first displacement of bed material, Dg the effective diameter of the bed materials, d the depth of flow, γ^s' the submerged unit weight equals to ^g

(

^ρs−ρ

)

, g the acceleration due to gravity, ρs the mass density of the bed materials, ρ the mass density of the flowing fluid. Later the equation was modified to calculate the critical shear stress directly (Neill, 1973; Fairfax County, 2004):

( )

₅₀^{23 13}

0.76090 1

c Sg D d

τ = γ − (2.6) where, γ is the specific weight of water (N/m³), S^g the specific gravity of soil,and d the depth of flow (m).

As the above critical shear stress estimation is dependent on the depth of flow so the estimated critical shear stress in this case can not be considered as an exclusive soil property.

Based on the experimental results of Dunn (1959) and Vanoni (1977), Julian and Torres (2006) estimated the critical shear stress from percentage of silt and clay (SC) contents. In this equation, silt-clay contents are defined as the particles less than 0.63 mm:

( ) ( )

^{2 5}

( )

³

0.1 0.1779 0.0028 2.34 10

c SC SC SC

τ = + + − × ⁻ (2.7)

In the same study, to account for the vegetation effect, a multiplying factor (range, 1- 19.20) was used to increase the critical shear stress.

Although the flume studies allow much control over the experiments, but at the same time it involves lots of issues. The major issues are the disturbed soil structures and

the degree of compaction (Hanson et al., 1999; Hanson and Cook, 2004). Alternately, in situ experiments for determining the critical shear stress and the erodibility are advantageous. A submerged jet test device, designed by Hanson (1990a) allows better applicability for wide ranges of soils and environmental conditions. A water jet generated through a nozzle (diameter 6.4 mm) impacts on the soil surface. After impact, it diffuses radially and thus produces shear stress on the soil surface. Recent studies (Hanson and Cook, 1997; Hanson and Simon, 2001; Wynn, 2004) using this apparatus show the ranges of the critical shear stress and erodibility coefficients for different study sites. Only limitation is that, the test is only applicable to the cohesive soils only. Maximum scour depth and critical shear stress are estimated by fitting a hyperbolic logarithmic equation to the scour data using the method described by Blaisdell model (Blaisdell et al., 1981).

The soil erodibility coefficient (k_d) is determined by fitting the jet scour data to the excess stress equation using the least square method. Hanson and Simon (2001) based on their 83 experimental results showed that this erodibility coefficient is related to the critical shear stress through a power relation:

0.2 0.5

d c

k = τ⁻ (2.8) where, k_d is the erodibility coefficient (cm³/N-s). While, Wynn (2004) conducted 142 experiments in vegetated river bank at 25 field sites in southwest Virginia and found that these erodibility parameters are related through the following equation:

3.1 0.37

d c

k = τ⁻ (2.9) The erosion rate for the fine grained soils in river bed or river bank is generally assumed to be proportional to the excess shear stress and can be expressed in the form of following equation (Hanson, 1990a, b; Hanson and Cook, 1997):

( )^a

d a c

ε =k τ −τ (2.10) where, ε the rate of erosion (m/s), k_d the erodibility coefficient (m³/N-s), τa _the

developed shear stress at the soil boundary (Pa), a the exponent generally considered to be 1.

No such study till now has been carried out to determine the erodibility parameters in situ and compare the results with the existing empirical methods for the banks of the Brahmaputra river. Therefore, it is important to measure the in situ erodibility parameters for the banks of the river Brahmaputra. This is one of the critical parameters in bank erosion processes, which involve the uncertainty in measurements and spatial distribution.