Abstract
Impulse waves that are generated by landslides in narrow reservoir areas threaten the stability of buildings and bank slopes. To discuss the action process and evolution law of the wave pressure on bank slopes, a three-dimensional physical model test that considers impulse waves generated by landslides was performed, and factors including landslide width, thickness, slope angles of the sliding surface, and bank slope angle were considered. Based on wave forms on the bank slopes, wave pressure curve characteristics, and peak value, the action process of wave pressure could be divided into the following stages: maximum pulsating pressure stage, wave impact stage (when waves break), and stationary pulsation stage. It was found that wave breaking is dependent on the value of the surf similarity parameter ξ. The distribution pattern of impact pressure decays linearly on both sides of the maximum impact pressure point, and the attenuation degree decreases when it attains 40% of the maximum value. Thus, it is proposed that the prediction formula for the maximum effective impact pressure of the bank slope be related to the reciprocal of wave steepness, relative water depth, and slope rate. The prediction formula provides strong theoretical support for early safety warning and for predicting the bank slope under impulse waves generated by landslides.
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Availability of Data/Materials: The data that support the findings of this study are available from the first author (1214433724@qq.com) upon reasonable request.
Change history
08 April 2024
An Erratum to this paper has been published: https://doi.org/10.1007/s11629-024-8648-2
Abbreviations
- Abb. :
-
Explanation
- H :
-
Wave height
- L :
-
Wave length
- T :
-
Wave period
- g :
-
Acceleration due to gravity
- γ :
-
Water severity
- α :
-
Slide slope angle
- β :
-
Bank slope angle
- m :
-
Slope rate m=cotβ
- d :
-
Water depth at the toe of the slope
- R :
-
The maximum climb of waves
- P c1 :
-
The maximum wave pressure of the maximum pulsating pressure stage
- H 1 :
-
Wave height of the maximum wave corresponding to the maximum pulsating pressure stage at the toe of the slope
- T 1 :
-
Wave period of the maximum wave corresponding to the maximum pulsating pressure stage at the toe of the slope
- ξ :
-
Surf similarity parameter of the maximum wave corresponding to the maximum pulsating pressure stage at the toe of the slope \(\xi=1/m\sqrt{H_{1}/(\rm{g}T_{1}^{2}/2\pi)}\)
- H ims :
-
Effective wave height of wave impact stage
- L ims :
-
Effective wave length of wave impact stage
- P im :
-
Impact pressure of wave impact stage
- P ims :
-
Effective impact pressure: average value of the top 1/3 impact pressure in descending order
- P imsm :
-
The maximum effective impact pressure: maximum value of effective wave pressure distribution curve
- Z m :
-
Vertical height at which the maximum effective impact pressure acts with still water level as origin
- P i :
-
Pressure of point (zi, xi)
- Z i :
-
Vertical height with still water level as origin
- P :
-
Wave pressure on bank slope
- Z :
-
Vertical height of action point with still water level as origin
- Z o :
-
The maximum effective impact pressure acting point
- Z1 :
-
The underwater distribution curve inflection point
- Z 2 :
-
The above-water distribution curve inflection point
- Z 3 :
-
The maximum climbing high point position
- Z 4 :
-
The underwater pressure 0 point
- d/H ims :
-
Relative effective water depth
- P imsm/γL ims :
-
Relative maximum effective impact pressure of wave impact stage
- L ims/H ims :
-
The reciprocal of effective wave steepness of wave impact stage
- Z m/L ims :
-
Relative maximum effective impact pressure action point relative to effective wave length of wave impact stage
- Z i/Z m :
-
Relative position relative to the position of the maximum effective action point
- P i/P imsm :
-
Relative pressure relative to the maximum effective impact pressure
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Acknowledgments
This research was funded by Chongqing Municipal Education Commission Project under Grant No. KJQN202000747, the National Key Research and Development Program Project NO.2018YFB1600400, the China Postdoctoral Science Foundation funded project grant No.2019M663890XB, Chongqing Postdoctoral Science Foundation funded project Grant No. 228512. Natural Science Foundation of Chongqing No. cstc2019jcyj-msxmX0599.
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CAO Ting: Conceptualization, Methodology, Formal analysis, Investigation, Resources, Data Curation, Writing — Original Draft, Writing — Review & Editing, Visualization, Funding acquisition. WANG Pingyi: Conceptualization, Supervision, Project administration, Writing- Reviewing and Editing, Funding acquisition. QIU Zhenfeng: Investigation, Visualization, Investigation, Writing- Reviewing and Editing, Funding acquisition. LIU Jie: Writing — Review & Editing, Funding acquisition
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Cao, T., Wang, P., Qiu, Z. et al. Impact pressure of waves generated by landslides on bank slopes. J. Mt. Sci. 21, 918–931 (2024). https://doi.org/10.1007/s11629-023-8331-z
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DOI: https://doi.org/10.1007/s11629-023-8331-z