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A Numerical Study on Toppling Failure of a Jointed Rock Slope by Using the Distinct Lattice Spring Model

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Abstract

In this work, toppling failure of a jointed rock slope is studied by using the distinct lattice spring model (DLSM). The gravity increase method (GIM) with a sub-step loading scheme is implemented in the DLSM to mimic the loading conditions of a centrifuge test. A classical centrifuge test for a jointed rock slope, previously simulated by the finite element method and the discrete element model, is simulated by using the GIM-DLSM. Reasonable boundary conditions are obtained through detailed comparisons among existing numerical solutions with experimental records. With calibrated boundary conditions, the influences of the tensional strength of the rock block, cohesion and friction angles of the joints, as well as the spacing and inclination angles of the joints, on the flexural toppling failure of the jointed rock slope are investigated by using the GIM-DLSM, leading to some insight into evaluating the state of flexural toppling failure for a jointed slope and effectively preventing the flexural toppling failure of jointed rock slopes.

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Abbreviations

A D :

The representative area of a discontinuous spring bond

[C]:

The damping matrix

c D :

The cohesion of a discontinuous bond

c J :

The corresponding macroscopic joint parameters

E :

The Young’s modulus

E i :

The Young’s modulus of particle i

E j :

The Young’s modulus of particle j

\(\sum {{\mathbf{F}}_{j}^{(t)} }\) :

The total force applied to the particle

f n :

The normal spring force

F(t):

The external force vector

f D t :

The tensional strength

g_level :

The current gravity level

g_max :

The maximum gravity level for the simulation

g(t):

The gravity increase function

inter_Loop :

The number of iterations for the sub-calculation

Loop :

The index of the current iteration

[K]:

The stiffness matrix

k n :

The normal spring stiffness

k D n :

The normal spring stiffness of a discontinuous bond

k J n :

The macroscopic joint normal stiffness

k s :

The shear spring stiffness

k D s :

The shear spring stiffness of a discontinuous bond

k J s :

The macroscopic joint shear stiffness

[M]:

The mass matrix

diag([M]):

The diagonal elements of the mass matrix

max_Loop :

The maximum loop for the simulation

m p :

The mass of a particle

n TC :

The total number of spring bonds cut by the same triangle

S T :

The area of the triangle

∆t :

The time step

u :

The vector of particle displacement

u n D :

The discontinuous spring’s normal deformation vector

u s D :

The discontinuous spring’s shear deformation vector

u n :

The spring’s normal deformation

\({\dot{\mathbf{u}}}_{i}^{(t + \Delta t/2)}\) :

The particle velocity at t + ∆t/2

\({\dot{\mathbf{u}}}_{i}^{(t - \Delta t/2)}\) :

The particle velocity at t − ∆t/2

u (t+Δt) i :

The displacement at t + ∆t

u (t) i :

The displacement at t

u * t :

The ultimate tensional deformation of the spring

ν:

The Poisson’s ratio

ν i :

The Poisson’s ratio at particle i

ν j :

The Poisson’s ratio at particle j

V :

The volume of the geometry model

α3D :

The lattice coefficient of a computational model

ϕ D :

The internal friction angle of the discontinuous spring bond

ϕ J t :

The macroscopic joint friction angle

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Acknowledgements

The research was financially supported by the National Key Research and Development Programme of China (2016YFC0401905), National Natural Science Foundation of China (51379140), and the State Key Laboratory for Geomechanics and Deep Underground Engineering, CUMT (Grant No. SKLGDUEK1706).

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Authors and Affiliations

  1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, School of Civil Engineering, Tianjin University, Tianjin, 300072, China

    Ji-Jian Lian, Qin Li & Gao-Feng Zhao

  2. China Railway No. 4 Group Co., Ltd, Hefei, 230023, Anhui, China

    Xi-Fei Deng

  3. School of Transportation Science and Engineering, Beihang University, Beijing, 100191, China

    Zu-Yu Chen

  4. Department of Geotechnical Engineering, China Institute of Water Resources and Hydropower, Beijing, 100048, China

    Zu-Yu Chen

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  1. Ji-Jian Lian
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  2. Qin Li
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  3. Xi-Fei Deng
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  4. Gao-Feng Zhao
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  5. Zu-Yu Chen
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Correspondence to Qin Li.

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Lian, JJ., Li, Q., Deng, XF. et al. A Numerical Study on Toppling Failure of a Jointed Rock Slope by Using the Distinct Lattice Spring Model. Rock Mech Rock Eng 51, 513–530 (2018). https://doi.org/10.1007/s00603-017-1323-y

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  • DOI: https://doi.org/10.1007/s00603-017-1323-y

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