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Laboratory study on relative energy loss and backwater rise at bridge piers and abutment

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Abstract

The presence of bridge structures in river channels can act as obstacles against flow and create backwater upstream. Therefore, to predict and identify flood areas under a certain discharge, accurate estimation of water surface profiles, (WSPs), relative energy loss, and backwater rise are essential. The present study utilized flume experiments to explore the effects of (1) approach flow conditions,(2) contraction ratios, (3) the distance between bridge piers and abutment, and (4) the distance between bridge piers on water surface profiles (WSPs), relative energy loss, and backwater rise at bridge piers and abutment. Moreover, this study incorporated, for the first time, the relative distances between bridge piers and abutment, as well as between bridge piers, in estimating water surface profiles (WSPs), relative energy loss, and backwater, based on a comprehensive literature review. The experiments showed that the contraction ratio, Froude number, relative distance between bridge pier and abutment, and relative distance between bridge piers were the most significant parameters influencing relative energy loss and backwater rise, respectively. Furthermore, this study developed two new equations for predicting relative energy loss and backwater rise at the interaction between bridge piers and abutment. The accuracy of the backwater equation was evaluated using laboratory data and compared with existing equations in the literature. The comparison showed that the existing equations overestimate backwater rise around bridge piers and abutment and had lower correlation coefficients (\({R}^{2}\)) than the proposed equation.

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Data availability

Data used in this study will be made available from the corresponding author on request.

Abbreviations

\({{\rm F}}_{3\mathrm{c}}\) :

Downstream Froude number \(\left(-\right)\)

\({{\rm Fr}}_{0}\) :

Approach flow Froude number \(\left(-\right)\)

\({{\rm K}}_{\mathrm{DA}}\) :

D’Aubuisson pier shape \(\left(-\right)\)

\({{\rm K}}_{\mathrm{N}}\) :

Nagler pier shape \(\left(-\right)\)

\(\upbeta \) :

Correction factor \(\left(-\right)\)

\({\updelta }_{0}\) :

Rehbock pier shape \(\left(-\right)\)

\(\mathrm{\alpha }\) :

Contraction ratio \(\left(-\right)\)

\(\mathrm{K}\) :

Yarnell pier shape ( − )

\(\mathrm{M}\) :

Opening ratio ( − )

\({\mathrm{y}}_{1}/{\mathrm{y}}_{0}\) :

Relative depth \(\left(-\right)\)

\(\mathrm{V}\) :

Flow velocity \((m/s)\)

\(\mathrm{F}\) :

Froude number \(\left(-\right)\)

\(\mathrm{B}\) :

Channel width \(\left(m\right)\)

\(\mathrm{\varphi }\) :

Al-Nassri pier shape \(\left(-\right)\)

\(\mathrm{\alpha }\) :

Kinetic energy correction coefficient \(\left(-\right)\)

L*:

Maximum length of backwater \(\left(m\right)\)

\({\mathrm{u}}_{0}\) :

Approach flow velocity \((m/s)\)

\({\mathrm{Q}}_{0}\) :

Discharge \(\left({m}^{3}/s\right)\)

\({\mathrm{h}}_{0}\) :

Normal flow depth \(\left(m\right)\)

\(g\) :

Gravitational acceleration \(\left(m/{s}^{2}\right)\)

ρ:

Water density \(\left(kg/{m}^{3}\right)\)

σ:

Water surface tension \(\left(kg/{s}^{-2}\right)\)

v :

Kinematic viscosity \(\left({m}^{2}/{s}^{-1}\right)\)

\({\mathrm{L}}_{\mathrm{a}}\) :

Abutment length \(\left(m\right)\)

\({\mathrm{B}}_{\mathrm{a}}\) :

Abutment width \(\left(m\right)\)

\({\mathrm{D}}_{\mathrm{p}}\) :

Pier diameter \(\left(m\right)\)

\({\mathrm{n}}_{\mathrm{p}}\) :

Pier number \(\left(-\right)\)

\(x\) :

Distance between bridge pier and abutment \(\left(m\right)\)

\(\mathrm{G}\) :

Distance between bridge piers \(\left(m\right)\)

\({\mathrm{E}}_{0}\) :

Energy loss related to the normal depth \(\left(m\right)\)

\(\Delta \mathrm{h}\) :

Backwater rise variation \(\left(m\right)\)

\(\Delta \mathrm{E}\) :

Energy loss variation \(\left(m\right)\)

\(\Delta \mathrm{h}/{\mathrm{h}}_{0}\) :

Relative backwater rise \(\left(-\right)\)

\(\Delta \mathrm{E}/{\mathrm{E}}_{0}\) :

Relative energy loss \(\left(-\right)\)

\(x/{\mathrm{D}}_{\mathrm{p}}\) :

Relative distance between the bridge pier and abutment \(\left(-\right)\)

\(\mathrm{G}/{\mathrm{D}}_{\mathrm{p}}\) :

Relative distance between the bridge piers \(\left(-\right)\)

\(\text{Cr}\) :

Contraction ratio \(\left(-\right)\)

WSPs:

Water surface profiles \(\left(-\right)\)

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Acknowledgements

The authors gratefully acknowledge the financial support for this work that was provided by financial support by Iran National Science Foundation (INSF) [grant number: 99017275].

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Authors and Affiliations

  1. Department of Civil Engineering, Semnan University, Semnan, Iran

    Saba Soori & Hojat Karami

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  1. Saba Soori
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  2. Hojat Karami
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Correspondence to Hojat Karami.

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Soori, S., Karami, H. Laboratory study on relative energy loss and backwater rise at bridge piers and abutment. Model. Earth Syst. Environ. 10, 1359–1373 (2024). https://doi.org/10.1007/s40808-023-01830-2

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  • DOI: https://doi.org/10.1007/s40808-023-01830-2

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