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The influence of upstream slope on the local scour at drop structure

  • Geological Egineering
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Abstract

The drop structure will fail as a result of local scoring downstream. This paper discusses the influence of a drop structures’ upstream slope to local scour. Empirical equations of the scour hole were developed by laboratory experiment, theoretical assumptions, and regression analysis. These equations include the maximum scour depth and length during the scouring period, the maximum equilibrium scour depth and length, and the unit width scour rate. The four channel slopes (0%, 2%, 4%, and 6%) before the drop structure has been included in the analysis. A series of laboratory experiments were conducted to obtain 48 groups of experiments and 419 scour hole profiles during the scouring period. The material used in the scour section is uniform non-cohesive and with a median diameter of d 50 = 0.5 mm. The results have been used to develop empirical equations via regression analysis to determine the coefficients of theoretical equations. The high correlation coefficient indicates that the equations developed in this study are suitable for verifying the characteristics of a scour hole at drop structure in the sloped channel. The semi-empirical equation is more accurate than the empirical equation. Compared to a horizontal channel, a sloped channel tends to cause a greater equilibrium maximum scour length, shorter equilibrium maximum scour depth, and faster unit-wide scour rate.

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Abbreviations

A s :

Dimensionless unit-wide scour volume of the scour hole profile -

A st :

Scour hole area at a given duration L 2

A se :

Scour hole area at equilibrium scour state L 2

C 1 :

the shape coefficient -

C 2 :

the distance coefficient -

D :

Downstream channel grain size L

DSR:

Dimensionless scour rate of unit width -

EMSD:

Equilibrium maximum scour depth L

EMSL:

Equilibrium maximum scour length L

g :

Gravitational acceleration L 2 T −1

h :

Drop height L

h se :

The EMSD L

h st :

The maximum scour depth at a given time duration L

h t :

Tail water height L

L it :

The horizontal distance from the toe of the drop structure to the EMSD L

L st :

The horizontal distance from the toe of the drop structure to the MSD at a given time duration L

MSD:

Maximum scour depth L

MSL:

maximum scour length L

N d :

Drop Number -

q :

Unit-wide discharge L 2 T −1

q se :

Mean unit-wide scouring rate for the duration from the beginning to the end of scour development L 2 T −1

q st :

Unit-wide scouring rate at a given duration L 2 T −1

S :

Slope of the upstream channel -

t :

The duration since the scouring starts T

t e :

The duration since the equilibrium scour hole is developed T

T e :

Time of the equilibrium scour hole T

s :

Slope of the upstream channel -

SR:

Scour rate of unit width L 2 T −1

UBS:

Upstream bed slope -

β :

Slope factor -

δ :

Slope-effect ratio -

λ :

Scouring process factor -

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Acknowledgment

The authors would like to appreciate the research support from Ministry of Science and Technology of Chinese Taipei, with the project no. 104-2313-B-343-001.

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Authors and Affiliations

  1. Department of Civil Engineering, National Chung Hsing University, Taichung, 40227, Taiwan, Province of China

    Jen-yan Chen & Hsi-hsin Hsu

  2. College of Management, Nanhua University, Chiayi County, 62249, Taiwan, Province of China

    Yao-ming Hong

Authors
  1. Jen-yan Chen
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  2. Hsi-hsin Hsu
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Correspondence to Yao-ming Hong.

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http://orcid.org/0000-0003-3336-0558

http://orcid.org/0000-0001-8943-411X

http://orcid.org/0000-0002-9007-3347

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Chen, Jy., Hsu, Hh. & Hong, Ym. The influence of upstream slope on the local scour at drop structure. J. Mt. Sci. 13, 2237–2248 (2016). https://doi.org/10.1007/s11629-015-3790-5

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  • DOI: https://doi.org/10.1007/s11629-015-3790-5

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