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Numerical Modeling of Earthquake-Induced Landslide Using an Improved Discontinuous Deformation Analysis Considering Dynamic Friction Degradation of Joints

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Abstract

Discontinuous deformation analysis (DDA) as an efficient technique has been extensively applied in the dynamic simulation of discontinuous rock mass. In the original DDA (ODDA), the Mohr–Coulomb failure criterion is employed as the judgment principle of failure between contact blocks, and the friction coefficient is assumed to be constant in the whole calculation process. However, it has been confirmed by a host of shear tests that the dynamic friction of rock joints degrades. Therefore, the friction coefficient should be gradually reduced during the numerical simulation of an earthquake-induced rockslide. In this paper, based on the experimental results of cyclic shear tests on limestone joints, exponential regression formulas are fitted for dynamic friction degradation, which is a function of the relative velocity, the amplitude of cyclic shear displacement and the number of its cycles between blocks with an edge-to-edge contact. Then, an improved DDA (IDDA) is developed by implementing the fitting regression formulas and a modified removing technique of joint cohesion, in which the cohesion is removed once the ‘sliding’ or ‘open’ state between blocks appears for the first time, into the ODDA. The IDDA is first validated by comparing with the theoretical solutions of the kinematic behaviors of a sliding block on an inclined plane under dynamic loading. Then, the program is applied to model the Donghekou landslide triggered by the 2008 Wenchuan earthquake in China. The simulation results demonstrate that the dynamic friction degradation of joints has great influences on the runout and velocity of sliding mass. Moreover, the friction coefficient possesses higher impact than the cohesion of joints on the kinematic behaviors of the sliding mass.

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Abbreviations

D(t):

Dynamic friction degradation coefficient of joints

η(t):

Friction strength ratio

γ(t):

Influence coefficient of relative velocity

δ(t):

Convergence value of the friction strength ratio η(t)

a :

A constant determined by cyclic shear test

K(t):

Number of shear displacement cycles

b :

A constant determined by cyclic shear test

R 0 :

Convergence value of δ(t)

J(t):

Amplitude of the cyclic shear displacement

m :

A constant determined by shaking table test

P 0 :

A convergence value of γ(t)

φ 0 :

Initial internal friction angle of joint

φ(t):

Internal friction angle of joint at time t

u 0 :

x translation of the block centroid (x 0, y 0)

v 0 :

y translation of the block centroid (x 0, y 0)

γ 0 :

Rigid rotation around the block centroid (x 0, y 0)

\(\left( {\begin{array}{*{20}c} {\varepsilon_{x} } & {\varepsilon_{y} } & {\gamma_{xy} } \\ \end{array} } \right)\) :

Normal and shear strains of block

T i :

Displacement transformation matrix of the block i

[K]:

Global stiffness matrix of the whole system formed by n blocks

[K ii ]:

Stiffness of the block i

[K ij ] [K ji ]:

Contact stiffness between blocks i and j. [K ij ] is the contact stiffness of block j acting on block i, and [K ji ] is that of block i acting on block j

M :

Mass matrix

C :

Dam** matrix

F :

Force vector

\(\ddot{D}\) :

Acceleration vector

\(\dot{D}\) :

Velocity vector

D :

Displacement vector

a H :

Horizontal dynamic acceleration

a V :

Vertical dynamic acceleration

f :

Friction force

N :

Normal support force between blocks

a d :

Downward critical acceleration

a u :

Upward critical acceleration

V 1 :

Velocity of base block

V 2 :

Velocity of sliding block

a 2 :

Absolute acceleration of the sliding block

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Acknowledgments

This work is supported by National Natural Science Foundation of China (No 41472245), the Chongqing Graduate Student Research Innovation Project (No. CYB14018), the Fundamental Research Funds for the Central Universities (No. 106112016CDJZR208804) and the Scientific Research Foundation of State Key Lab. of Coal Mine Disaster Dynamics and Control (No. 2011DA105287-MS201502).

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Authors and Affiliations

  1. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400045, China

    Da Huang & Yixiang Song

  2. School of Civil Engineering, Chongqing University, Chongqing, 400044, China

    Da Huang, Yixiang Song & Duofeng Cen

  3. School of Engineering, RMIT University, Melbourne, 3001, Australia

    Guoyang Fu

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  1. Da Huang
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Huang, D., Song, Y., Cen, D. et al. Numerical Modeling of Earthquake-Induced Landslide Using an Improved Discontinuous Deformation Analysis Considering Dynamic Friction Degradation of Joints. Rock Mech Rock Eng 49, 4767–4786 (2016). https://doi.org/10.1007/s00603-016-1056-3

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