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Calculating the Permanent Displacement of a Rock Slope Based on the Shear Characteristics of a Structural Plane Under Cyclic Loading

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Abstract

When a rock mass shears along a structural plane, the shear resistance of the structural plane is affected by the structural plane undulations and by the friction between the contact regions. During an earthquake, the seismic load (composed of the cyclic and dynamic loads) produces a dynamic deterioration of the mechanical properties of the structural plane, which is mainly reflected as follows: (1) under cyclic shear of the seismic load, the undulant angle αk decreases. (2) Under the dynamic load, the frictional coefficient of the structural surface is reduced. The dilatancy angle is generally used instead of the undulant angle. When calculating rock slope stability, the frictional angle is equivalent to the sum of the basic frictional angle and the undulant angle. In this study, the equations for calculating the dilatancy angle of a structural plane under cyclic shear loading are determined based on cyclic shear tests of a split structural plane. The basic frictional angle for calculating the cyclic shear is also determined, based on previous research. Furthermore, according to the dynamic model of a rock slope, a method to calculate the permanent displacement of the rock slope is proposed, considering the effect of structural plane deterioration. We found that the effect of structural plane deterioration under a seismic load directly affects the stability and permanent displacement of the rock slope. The feasibility and engineering practicalities of this method are also verified by comparing the proposed method with previously developed methods.

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Abbreviations

R h :

Maximum height of the surface roughness profile

R p :

Maximum contour peak height

R v :

Maximum contour valley depth

S A :

Contour area ratio

A t :

Developed contour surface area

A n :

Sampling area

A c :

Structural surface contact area

JMC:

Joint Matching Coefficient

α i :

Average shear dilatancy angle

i :

Cyclic shear times

σ c :

Intact rock strength

α 0 :

Initial undulant angle

φ i :

Basic frictional angle

φ 0 :

Initial basic frictional angle

φ r :

Residual basic frictional angle

α r :

Residual undulant angle

\(\varphi_{{\text{s}}}^{*}\) :

Residual equivalent friction angle

C :

Cohesion

M :

Mass of the landslide

Β :

Dip angle of the sliding surface

\(\ddot{u}_{{\text{g}}}\) :

Seismic acceleration

θ:

Angle between the direction of the earthquake motion and the horizontal direction

F s :

Safety factor

φ b :

Basic frictional angle

α k :

Undulant angle

α d :

Dilatancy angle

JRC:

Roughness coefficient

a y :

Critical acceleration

k y :

Yield coefficient

g :

Gravitational acceleration∅

∅:

Frictional angle between the block and the plane

a :

Joint damage coefficient

(αk)0:

Initial undulant angle

W P :

Plastic work

ac(t):

Acceleration of the shaking table δ

δ:

An operator

x n :

Block displacement at time n∆t

x ac ∙ n :

Cumulative displacement at time n∆t

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Acknowledgements

The project was supported by The National Natural Science Foundation of China (Grant Number: 41977252); the Sichuan Provincial Youth Science and Technology Innovation Team Special Projects of China (Grant No. 2017TD0018); the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection of the Chengdu University of Technology Open Fund (Grant No. SKLGP2019K010); the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection of the Chengdu University of Technology Open Fund (Grant No. SKLGP2020K015); and the Team Project of Independent Research of SKLGP (Grant No. SKLGP2016Z001); the Key Technology Projects of Transportantion Industry in 2018 (Grant No. 2018-ZD5-029).

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  1. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, 610059, CN, China

    Shan Dong, Wenkai Feng, Yibo Yin, Rui Hu, Hongchuan Dai & Guoqiang Zhang

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  1. Shan Dong
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  2. Wenkai Feng
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Correspondence to Wenkai Feng.

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Dong, S., Feng, W., Yin, Y. et al. Calculating the Permanent Displacement of a Rock Slope Based on the Shear Characteristics of a Structural Plane Under Cyclic Loading. Rock Mech Rock Eng 53, 4583–4598 (2020). https://doi.org/10.1007/s00603-020-02188-y

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