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Development of a Coupled DDA–SPH Method and its Application to Dynamic Simulation of Landslides Involving Solid–Fluid Interaction

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Abstract

Landslides involving solid–fluid interaction such as submarine landslides and landslide dams occur frequently around the world, which may bring severe damage to human lives and properties. Investigation of such landslides is thus of significance to hazard prevention and mitigation. To conduct the analysis, there are three key points to be addressed: (a) the landslide failure process, (b) the free surface flow, and (c) the solid–fluid interaction process. Discontinuous deformation analysis (DDA) method is suitable for analyzing discontinuous blocky systems and has outstanding advantages in simulating the landslide failure process. Meanwhile, smoothed particle hydrodynamics (SPH) method is well-suited for modeling the free surface flow. However, the consideration of solid–fluid interaction in these two methods is seldom, which somehow restricts their applications. With the aim to take advantages of these two methods, a coupled DDA–SPH method in two-dimensional case is proposed, in which the solid–fluid interaction is forced using a penalty approach. The SPH formulations are implemented into DDA code. Several numerical examples are presented to check the validity of the proposed method. A dam-break test is first investigated to show the success of implementing SPH into DDA code for modeling the fluid flow in later simulations of fluid–solid systems. Subsequently, the performance of the coupled DDA–SPH method is validated through a submarine rigid landslide, and the simulation results are in good agreement with the experimental data. Further, an extension study on the submarine deformable landslide is performed, in which the landslide mass consists of multiple blocks and a sensitivity analysis on the interface friction angle between blocks is conducted. Finally, a designed landslide dam is simulated to show the applicability and feasibility of the coupled DDA–SPH method.

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Abbreviations

D i :

Deformation matrix of block i

x0, y0 :

Coordinates of block centroid

u0, v0 :

Displacements of block centroid

r 0 :

Rigid body rotation

εx, εy, γxy :

Constant strains of block

u, v :

Displacements of point P(x, y)

Ti (x, y):

Displacement transformation matrix of point P(x, y) on block i

n :

Total number of blocks

Kij (i, j = 1, 2,…, n):

6 × 6 stiffness submatrices

F i :

6-Member load vectors

x :

Location vector of a point

f(x):

A field function

Ω :

Integration domain (the support domain)

W(\(\varvec{x} - \varvec{x'}\), h):

Smoothing function

h :

Smoothing length

α D :

Normalization factor

R :

Normalized distance defined as R = |\(\varvec{x} - \varvec{x'}\)|/h

m j :

Mass of particle j

ρ j :

Density of particle j

N :

Total number of neighboring particles

xi, xj :

Location vectors of particles i and j

r ij :

Distance between particle i and j

κ :

A constant coefficient

α, β :

Coordinate dimensions with the Einstein convention

t :

Time

ρ :

Density

x α :

Location component

v α :

Velocity component

σ αβ :

Total stress tensor

f α :

Acceleration component induced by external forces

Π ij :

Artificial viscosity

\(\alpha_{\varPi }\) :

Artificial viscosity coefficient

c :

Sound speed

ρ 0 :

Reference density

c 0 :

A numerical speed of sound

γ :

A dimensionless parameter

δ :

Diffusive coefficient

r 10 :

Auxiliary vector

P 12 :

Connection vector P12 between the vertices P1 and P2

λ :

Scale factor

P c :

Possible contact point

δ n :

Distance between SPH particle and its contact point on block

n :

Unit normal vector of an edge

F :

Contact force exerted on a fluid particle

Fn, Fτ :

Normal and tangential components of the contact force

k s :

Penalty stiffness

k d :

Damping coefficient

d sf :

Penetration distance

k f :

Friction coefficient

τ :

Normalized tangential vector of a contact edge

Δd :

Particle spacing

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant numbers 41672286 and 51408511), Science & Technology Department of Sichuan Province (Grant number 2017JQ0042), the SKLGP open fund (SKLGP2018K009), JSPS KAKENHI (Grant numbers JP15K12483, JP16F16056, and JP15H01797), the Japanese Government (MEXT) Scholarship Program, and the China Scholarship Council (CSC). The financial supports are gratefully acknowledged. The authors also appreciate the editor and reviewers for their helpful and insightful comments that greatly improved the manuscript.

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Authors and Affiliations

  1. Department of Civil and Structure Engineering, Kyushu University, Fukuoka, 8190395, Japan

    Xinyan Peng, Pengcheng Yu, Guangqi Chen & Mingyao Xia

  2. Department of Geotechnical Engineering, School of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Yingbin Zhang

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  1. Xinyan Peng
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Correspondence to Pengcheng Yu.

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Peng, X., Yu, P., Chen, G. et al. Development of a Coupled DDA–SPH Method and its Application to Dynamic Simulation of Landslides Involving Solid–Fluid Interaction. Rock Mech Rock Eng 53, 113–131 (2020). https://doi.org/10.1007/s00603-019-01900-x

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