# Accuracy of Equivalent Roughness Height Formulas in Practical Applications

^{1}

## Summary (1 min read)

### Introduction

- Estimating bedload transport is of great importance for engineering design and morphodynamic modelling; yet bedload transport rate predictions are based on insufficient understanding of the resistance to flow in alluvial channels.
- Most of the formulas were validated for fine sediments and high shear stresses.
- The flow seems to be affected by the bed load transport for these particular cases as much as in the sheet flow transport cases.
- The main objective of the present study is to highlight these problems induced by the iterative method.

### Iterative procedure

- The iterative solution can be expressed using the relationship for the friction coefficient (see Eq. 12 in Camenen et al., 2006) and the definition of the Shields parameter (see Eq. 2 in Camenen et al., 2006) .
- Thus, the Shields parameter can be expressed 5 Author-produced version of the article published in J. Hydraul.
- The original publication is available at http://ascelibrary.org.

### Graphical interpretation of the iterative procedure

- The iterative method will never induce a better result compared to the fitted curve because the two curves f and F −1 are increasing functions of θ.
- A slight underestimation is observed using the fitted curve.

### Fig. 2 here

- In conclusion, it appears that the iterative method is not very accurate from a practical point of view.
- A solution does not always exist, and most of the time, two solutions coexist.
- If there is an error between the data and the fitted curve, it will necessarily be larger after employing the iterative method.

### Tab. 1 here

- The iterative solution for a pair (k s , θ) 9 Author-produced version of the article published in J. Hydraul.
- The original publication is available at http://ascelibrary.org.
- As a matter of fact, the accuracy of the results (P 2) drops with 10% to 30% depending on the formula used (cf. table 1 and Fig Shields parameter, which are underestimated.

### Conclusions

- Many formulas have been proposed to estimate the roughness height in the case of plane beds.
- All the previous authors proposed equations assuming that the total Shields parameter is already known.
- And reveal the main factors governing roughness, they are not applicable from an engineering point the view.
- The iterative formulas resulting from these equations yields very large scatter in the results.
- Finally, the use of the skin Shields parameter produces nearly as good results, apart for large values of the total Shields parameter, which are underestimated.

Did you find this useful? Give us your feedback

##### Citations

83 citations

9 citations

### Cites background from "Accuracy of Equivalent Roughness He..."

...Miedema and Ramsdell (2016) and Camenen and Larson (2013) have concluded that Equation 3....

[...]

6 citations

### Cites methods from "Accuracy of Equivalent Roughness He..."

...…these structures with straight and transitional virtual channels without considering the detailed flow inside the structure, and the equivalent roughness method proposed by Camenen and Larson (2013) can be used to replace local head loss and then the roughness can be calculated using measured data....

[...]

5 citations

### Cites background from "Accuracy of Equivalent Roughness He..."

...lished from Huthoff’s results and the decisive factor affecting the equivalent roughness is still unclear [18]....

[...]

##### References

2,182 citations

### "Accuracy of Equivalent Roughness He..." refers background in this paper

...2006) or of bed-load transport rate, if the latter is assumed to be directly related to the Shields parameter (Meyer-Peter and Müller 1948)....

[...]

...1(a) corresponds to an experimental case from Smart (1984); Fig....

[...]

...Meyer-Peter and Müller (1948) introduced a lin-21 ear decomposition of the total resistance coefficient, which may be rewritten22 as a linear decomposition of the total bed roughness (Soulsby, 1997; Came-23 nen et al., 2006).24 Excluding form drag, the value of the equivalent roughness height ks…...

[...]

1,962 citations

### "Accuracy of Equivalent Roughness He..." refers background in this paper

...…plane bed regime, where ks is not46 only a function of the median grain size d50 but also of θ (Wilson, 1966; Nnadi47 and Wilson, 1992; Yalin, 1992; van Rijn, 1993; Sumer et al., 1996; Bayram48 et al., 2003; Camenen et al., 2006) or of bedload transport rate, if the latter49 is assumed to be…...

[...]

...…+ z0)/R ln ((R + z0)/z0)− 1 ]2 Uc 2 (s− 1)gd50 (1) Employing the relationships proposed by different authors (Wilson, 1966; Yalin, 1992; van Rijn, 1993; Sumer et al., 1996; Bayram et al., 2003; Camenen et al., 2006), which can be expressed as ks/d50 = f(θ), equation 1 can easily be…...

[...]

1,178 citations

### "Accuracy of Equivalent Roughness He..." refers background in this paper

...…a lin-21 ear decomposition of the total resistance coefficient, which may be rewritten22 as a linear decomposition of the total bed roughness (Soulsby, 1997; Came-23 nen et al., 2006).24 Excluding form drag, the value of the equivalent roughness height ks still25 varies considerably…...

[...]

362 citations

### "Accuracy of Equivalent Roughness He..." refers background in this paper

...If ks is generally assumed to be proportional to a characteristic bed grain size (Bathurst 1985), several authors showed a significant increase in ks when bed-load transport occurs, even for coarse sediments (Campbell et al....

[...]

292 citations

### "Accuracy of Equivalent Roughness He..." refers background or methods in this paper

...1) for two particular cases: figure (a) corresponds102 to an experimental case from Smart (1984); figure (b) corresponds to an103 experimental case from Nnadi and Wilson (1992).104 Fig....

[...]

...cases: (a) experimental data from Smart (1984); (b) experimental data...

[...]