, Volume 15, Issue 10, pp 2083–2091 | Cite as

Application of incomplete similarity theory to the estimation of the mean velocity of debris flows

  • Tao Wang
  • Jiangang Chen
  • Xiaoqing ChenEmail author
  • Yong You
  • Niansheng Cheng
Technical Note


The mean velocity of debris flow is one of the most important parameters in the design of mitigation structures and in quantitative risk analysis. This study develops a model to predict the mean debris flow velocity observed in the field by applying the incomplete similarity argument. An equation for estimating the Darcy-Weisbach resistance coefficient for debris flows with a volumetric sediment concentration larger than 0.19 is accordingly derived using 128 sets of observation data from nine Chinese gullies, in which both the effect of the volumetric sediment concentration and channel slope on resistance are considered. The derived equation is then verified and compared against five previously published equations by using 61 sets of published observation data from six gullies located in four countries. The applications of the proposed equation are discussed, and the improvements made using the proposed equation are clearly very significant when compared with the previously published equations.


Debris flow Mean velocity Channel slope Volumetric sediment concentration Incomplete similarity 



We would like to thank the reviewers and editors for their comments.

Funding information

This study was supported by the National Science Foundation of China (Grant No. 41661134012, Grant No. 51409243, Grant No. 41671112).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Tao Wang
    • 1
    • 2
  • Jiangang Chen
    • 1
    • 2
  • Xiaoqing Chen
    • 1
    • 2
    Email author
  • Yong You
    • 1
    • 2
  • Niansheng Cheng
    • 3
  1. 1.Key Laboratory of Mountain Hazards and Surface ProcessesChinese Academy of SciencesChengduChina
  2. 2.Institute of Mountain Hazards and EnvironmentChinese Academy of SciencesChengduChina
  3. 3.School of Civil and Environmental EngineeringNanyang Technological UniversitySingaporeSingapore

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