Abstract
This paper represents a numerical study on the effects of landslide initial submergence and its geotechnical and rheological properties on the characteristics of landslide-generated waves (LGWs) and landslide deformation. A number of 117 numerical experiments are performed using a two-layer Coulomb Mixture Flow (2LCMFlow) model on a real-sized numerical flume as a simplified cross section of the Maku dam reservoir, located in the Northwest of Iran. Three different initial locations are considered for landslide representing a subaerial (SAL), a semi-submerged (SSL), and a submarine (SML) landslide. Based on the numerical results, the majority of SMLs and in some cases SSLs generate tsunami waves with a larger wave trough than the wave crest. The maximum negative wave amplitudes of LGWs caused by SMLs (SMLGWs) can be up to 55% larger than that for SALs. LGWs caused by SALs (SALGWs) commonly have a higher wave crest than the wave trough. In 70% of cases, the maximum wave crests of SALGWs are larger than that for LGWs caused by SSLs (SSLGWs) and SMLGWs. While, in the rest 30% of simulations, the maximum SSLGW crests are up to 60% larger than SALGWs. Due to the landslide inter-phase interactions in combination with its basal and internal friction resistances, only 10–40% of the SAL initial mass contributes in LGW generation process. Energy transfer from landslide into water is about 0.5–7.5% for SMLs, 6–17.2% for SSLs, and 5–15% for SALs. The final deposit of SMLs generally has a short and thick profile while SALs and SSLs elongate more and travel longer distances. Finally, a Coulomb mixture product parameter, PCM, is defined to relate the maximum LGW heights to the considered landslide properties.
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Abbreviations
- A :
-
Jacobean matrix
- A s :
-
Landslide volume per unit width
- a n :
-
Negative wave amplitude
- a p :
-
Positive wave amplitude
- B :
-
Coupling term matrix
- b :
-
Bottom level
- C:
-
Characteristic wave velocity
- D :
-
Diagonal matrix of eigenvalues
- ET :
-
Energy conversion ratio
- E :
-
Total energy
- F :
-
Numerical flux matrix
- Fr :
-
Slide Froude number
- df :
-
Generalized numerical flux
- G :
-
General function
- g :
-
Gravitational acceleration
- H :
-
Wave height
- h :
-
Depth
- h 0 :
-
Still water depth
- h 1 :
-
Water layer depth
- h 2 :
-
Landslide thickness
- h max :
-
Maximum thickness of landslide deposit
- h s :
-
Front thickness of landslide at impact
- i :
-
i-th grid cell
- K :
-
Earth pressure coefficient
- KE :
-
Kinetic energy
- κ :
-
Matrix of local eigenvectors
- L s :
-
Landslide initial length
- l s :
-
Horizontal length of landslide deposit
- M :
-
Relative slide mass
- M w :
-
Moment magnitude of earthquake
- m :
-
Mass
- n :
-
Number of time steps
- P :
-
Pressure
- P 1 :
-
Roe correction term
- P 2 :
-
Corrected part of the projection matrixes
- P CM :
-
Coulomb mixture product parameter
- P I :
-
Impulse product parameter
- P zz :
-
Normal pressure
- PE :
-
Potential energy
- q :
-
Flow discharge (hu)
- R 2 :
-
Coefficient of determination
- r :
-
Relative density ρ2/ρ1
- r C :
-
Δt/Δx
- S :
-
Source term matrix
- S r :
-
Relative slide thickness
- T :
-
Coulomb friction matrix
- T S :
-
Landslide initial thickness
- t :
-
Time
- u :
-
Averaged velocity in x direction
- u s :
-
Landslide impact velocity
- s :
-
Landslide thickness at impact
- VS :
-
Landslide volume
- ν :
-
Velocity
- W :
-
Vector of unknowns
- w :
-
Water body width
- X :
-
Total length of computational domain
- x :
-
Cartesian coordinate horizontal component
- x 0 :
-
Horizontal coordinate of runup surface
- x ave :
-
Averaged location of landslide deposit
- x front :
-
Front location of landslide deposit
- x rear :
-
Rear location of landslide deposit
- z :
-
Cartesian coordinate vertical component
- Z 0 :
-
Landslide initial submergence depth
- δ :
-
Basal friction angle
- δ 0 :
-
Angle of repose
- δ mod :
-
Modified δ
- ψ 0 :
-
Landslide porosity
- η :
-
Water surface fluctuations
- θ :
-
Slope angle
- Λ 1 :
-
Parameter (λ1 + K(1 − λ1))
- Λ 2 :
-
Parameter (rλ2 + K(1 − rλ2))
- λ ′ :
-
Empirical parameter
- λ 1 :
-
Constitutive coefficient
- λ 2 :
-
Constitutive coefficient
- ρ 1 :
-
Water density
- ρ 2 :
-
Landslide bulk density
- ρ s :
-
Landslide solid grain density
- σ c :
-
Basal critical stress
- ϕ :
-
Internal friction angle
- ℑ :
-
Coulomb friction term
- τ crit :
-
Basal critical friction
- ∆t :
-
Time step
- ∆x :
-
Grid size in x direction
- Γl :
-
Local eigenvalues
- f :
-
Landslide fluid phase
- s :
-
Landslide solid phase
- \( \overline{} \) :
-
Roe intermediate state
- ∗ :
-
Predicted value of a parameter
- s :
-
Landslide property
- w :
-
Wave property
- 2LCMFlow:
-
Two-layer Coulomb mixture flow model
- 2D:
-
Two-dimensional
- 3D:
-
Three-dimensional
- EGT:
-
Earthquake-generated tsunami
- LGW:
-
Landslide-generated wave
- SAL:
-
Subaerial landslide
- SALGW:
-
Subaerial landslide-generated wave
- SML:
-
Submarine landslide
- SMLGW:
-
Submarine landslide-generated wave
- SSL:
-
Semi-submerged landslide
- SSLGW:
-
Semi-submerged landslide-generated wave
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Acknowledgements
The authors would like to thank the Civil Engineering Department of the Sharif University of Technology for their support during the completion of this research. The authors are also grateful for the constructive comments of the editor and two anonymous reviewers, which helped improving the final manuscript.
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Yavari-Ramshe, S., Ataie-Ashtiani, B. On the effects of landslide deformability and initial submergence on landslide-generated waves. Landslides 16, 37–53 (2019). https://doi.org/10.1007/s10346-018-1061-6
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DOI: https://doi.org/10.1007/s10346-018-1061-6