GENERATION OF STOCHASTIC HYDROGRAPH
5.4 Results and Discussion
0.53-1.95 cm3(N-s)-1 for Jamuguri, Dolgobinda bank site, Amingaon and red hilly soils, respectively.
(a)
0 0.2 0.4 0.6 0.8 1
0.1-1.0 1.0-10 10-100
tc (Pa)
Relative frequency
(b)
0 0.2 0.4 0.6 0.8 1
0.1-1.0 1.0-10 10-100
kd (cm3/N-s)
Relative frequency Jamuguri
Dolgobinda Red hills Amingaon Nalbari
Figure 5.6. Relative frequency of soil erodibility parameters. For (a) critical shear stress and (b) erodibility coefficient.
The test results for river bank locations demonstrate that the critical shear stress and the erodibility coefficient are inversely related. Hanson and Simon (2001) and Wynn (2004) both found a similar power relationship between these two parameters. It has been found from the jet test analysis; they follow the relationship described as:
0.185
3.16 c
kd = τ− (5.10) where, kd is the erodibility coefficient in cm3(N-s)-1 and τc is the critical shear stress in Pa. Initially, the equation was derived from the simple least square fitting method, which generates kd =2.447τc−0.04. The correlation between them was very poor (r2 = 0.0076).
However, it was found that there are a few outlier data points for which it is not possible to fit the data with simple regression. In this case robust regression technique gives a better fitting. This actually uses an iteratively re-weighted least square fitting method.
The weights at each iteration are calculated by applying the bi-square function to the residuals from the previous iteration. Thus this method gives less weight to the outliers and so the results are less sensitive to those outliers. As the robust regression is used for linear fitting equation, in this case, logs of both data has been taken and a higher correlation (p = 0.002) has been found. A similar trend of relationship was also reported by Wynn (2004), who found relationship askd =3.1τc−0.37. Hanson and Simon (2001) also reported a similar relationship between them although the coefficients are significantly different. A comparison between the relationship derived by Hanson and Simon (2001), Wynn (2004) and the present investigation is depicted in Figure 5.7, which shows a wide variation between the regression coefficients. This may be due to the fact that Hanson and Simon carried out their tests in the river bed, while the present study was carried out for the river banks. The vegetation cover in the river bank imparts some resistance to erodibility due to root spreading and thus ultimately influences the relationship between the erodibility parameters (Wynn, 2004).
Figure 5.7. Relationship between critical shear stress and erodibility coefficient.
To relate these erodibility parameters with the resistant or erodible nature of the river bank, a scatter plot between the critical shear stress and the erodibility coefficients is illustrated in Figure 5.8. This indicates that at Jamuguri, some bank locations are very erodible while other places are only moderately erodible. Similarly in Amingaon the banks also range from very erodible to moderately resistant. On the other hand, near Dolgobinda, the river banks are all found to be very erodible. However, the average trend of the red hilly soils indicates that they lie on the upper limit of the moderately resistant zone.
Figure 5.8. Classification of the river bank soil based on erodibility parameters (after Hanson and Simon, 2001).
Moreover, one dimensional ANOVA analysis was carried out for the erodibility parameters to test the locations and layer-wise dependency. Results show that the critical shear stress (Figure 5.9a) and erodibility coefficients (Figure 5.9b) are highly site specific (p value for critical shear stress and erodibility coefficients are 0.06 and 0.01, respectively). It means that the erodibility parameters vary significantly from one site to another. Figure 5.9a shows that critical shear stress values are quite similar for Dolgobinda and Amingaon, and also for Jamuguri and Nalbari. However, the ranges of critical shear stress for Jamuguri and Amingaon are wide. It can be observed from Figure 5.9b that the erodibility coefficient for the soil tested at Amingaon and the red soils are quite similar. So, for the estimation of the fluvial bank erosion it is important to estimate the local erodibility parameters of the bank soil.
ANOVA analysis is also carried out to test the dependency of the erodible parameters on the different layers of cohesive soils found at the site, (Figure 5.9c and 5.9d). However, the analysis shows that the erodibility parameters do not depend on the soil layers in a particular site. The p values for both the cases are very high (forτc, p
value= 0.967 and for kd, p value= 0.43), which indicates a poor relationship between the layers and the erodibility parameters. So for estimation of the fluvial erosion, layer-wise average erodibility parameters can be considered at a particular site.
Table 5.1 Estimates of the critical shear stress, median, and the ranges for different methods: Shields’ diagram (SD), median particle size (D50), percentage silt-clay content (SC) and percentage clay content
Method
τc (Pa)
Median Minimum Maximum
Jet test 2.14 0.007 23.34
SD (Shields’ 1936) 0.17 0.15 0.17
D50 (Smerdon and Beasley 1961) 3.52 3.50 3.53 SC (Julian and Torres 2006) 2.70 1.47 5.93
%Clay (Smerdon and Beasley 1961) 0.50 0.49 0.51
Figure 5.9. Spatial variation of erodibility parameters. For (a) critical shear stress on locations (p-value 0.060), (b) erodibility coefficient on locations (p-value 0.010), (c) critical shear stress on layers (p-value 0.967) and (d) erodibility coefficient on
Chapter 5: Erodibility of Fine Bank Soils 92
Critical shear stresses measured in situ using the jet testing, and the same estimated using Shields’ diagram (SD), median particle size (D50), percentage silt-clay content (SC) and the percentage clay content (%Clay) are presented in Table 5.1. Comparison of the data indicates the poor estimations using Shields’ diagram and % clay content. The one of the reasons is that Shields’ diagram was developed for non-cohesive particles with no consideration of the interaction between particles (Shields, 1936; Vanonni, 1977; Hann et al., 1994). On the other hand, because the clay content was found to be very small for the soils tested, the % clay content method also gives poor estimation of critical shear stress.
Estimation from percentage silt clay content method provides almost the same median value (2.70 Pa) as measured by the jet tests (2.14 Pa), while the median particle size estimation provides a slightly higher median value. However, the percentage silt clay content method can not assess the actual critical shear stress, as the water quality influences the soil erodibility (Clark and Wynn, 2007). For this reason submerged jet test method provides better estimate of critical shear stress under field conditions, while percentage silt clay content may be used as an alternative method for its approximate estimation.