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A three-dimensional large-deformation random finite-element study of landslide runout considering spatially varying soil

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Landslide is a uniquely dynamic large-deformation process that can present serious threat to human lives and infrastructures. The natural soil properties often exhibit inherent spatial variability, which affects the landslide behavior significantly. This paper focuses on combined Monte Carlo simulation and three-dimensional (3D) dynamic large-deformation finite-element (LDFE) analysis using the coupled Eulerian-Lagrangian method to investigate the whole runout process of landslide induced by the earthquake in spatially varying soil. The results from LDFE analysis show that the mean value of runout distance in spatially varying soil is significantly higher than that of the deterministic value obtained from a homogeneous slope due to the slope failure developed along the weakest path in soils. The mean runout distance increases and converges with increasing slope length in 3D-LDFE stochastic analysis. The advantages and necessities of 3D-LDFE analysis were illustrated by comparing it with two-dimensional (2D) LDFE analysis of landslide in spatially varying soil. The results show that the calculated mean runout distance using 3D-LDFE method is at least 16.1% higher than that calculated using 2D-LDFE analysis. Finally, a linear regression formula was established to estimate the mean runout distance of landslide due to horizontal inertia acceleration. Such a formula may facilitate the risk assessment of landslide in practical engineering.

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a :

Horizontal inertial acceleration

E :

Young’s modulus

f :

Field variable in Eulerian formulation

g :

Gravitational acceleration

h min :

The minimum mesh size used in CEL model

H :

Slope height

L 0 :

Slope length

L :

Runout distance

N :

The number of Monte Carlo simulation

S :

Source term in Eulerian formulation

s u0 :

Mean cohesion of soil

s u :

Spatially varying cohesion of soil

γ :

The unit weight of soil

θ :

Slope angle

φ :

Friction angle of soil

ψ :

Dilatancy angle of soil

ν :

Poisson’s ratio

ϕ :

Flux function in Eulerian formulation

Θ H :

Horizontal correlation length

Θ V :

Vertical correlation length


Peak ground acceleration


Two dimensional


Three dimensional


Coupled Eulerian-Lagrangian


Coefficient of variation


Eulerian volume fraction


Finite-element method


The factor of safety


The limit equilibrium method


Large-deformation finite element


Monte Carlo


The modified linear estimation method


Material point method


Remeshing and interpolation technique with small strain


Smoothed particle hydrodynamics


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This research is supported by the National Natural Science Foundation of China (Grant Nos. 51879203, 52079099). These supports are gratefully acknowledged.

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Correspondence to Yong Liu.

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Chen, X., Li, D., Tang, X. et al. A three-dimensional large-deformation random finite-element study of landslide runout considering spatially varying soil. Landslides 18, 3149–3162 (2021).

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