Abstract
Earthquakes have significant impact on rock slopes, thus studying the seismic stability of double-slider rock slopes containing tension cracks is crucial. We proposed an analysis method on the seismic dynamic slope stability. This method utilizes discrete Fourier transform to decompose real earthquake waves into a combination of harmonic waves. These waves are then used in conjunction with the pseudo-dynamic method and safety factor calculation formula to compute the safety factor. This approach accurately captures the influence of seismic time history characteristics on the dynamic stability of double-slider rock slopes containing tension cracks. The minimum safety factor in the obtained time history curves of the safety factor reflects the most unfavorable state of the slopes under seismic effects. Quantitative analysis is conducted using six sets of actual earthquake ground motion data obtained from the Pacific Earthquake Engineering Research Center’s NGAWest2 ground-shaking record database. The conclusions are as follows: (1) There is an inverse correlation between the average seismic acceleration amplitude and the minimum safety factor. Conversely, the seismic acceleration amplitude standard deviation shows a positive correlation with the minimum safety factor. The global sensitivity of geometric parameters in the slope model is higher than other influencing factors. (2) The proposed dynamic stability analysis method can capture the dynamic characteristics of earthquakes, emphasizing the minimum safety factor of the slope in the seismic time history as a stability indicator. In contrast, the pseudo-static method may yield unsafe results. (3) A safety factor expression considering hydrostatic pressure is proposed. A negative correlation was observed between the height of the water level line and the minimum safety factor.
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Data availability: All data included in this study are available upon request with the corresponding author.
Abbreviations
- a h(z,t), a v(z,t):
-
Horizontal and vertical acceleration at any depth z and time t
- A A and A B :
-
The area of contact of block A (B) and the failure
- c :
-
The cohesion of rock
- D :
-
Damping ratio
- E :
-
The elastic modulus of rock
- F driving and F resist :
-
The driving and resisting force of block
- FS:
-
Safety factor against plane failure mode
- FSA, FSB :
-
Safety factor of black A and B
- g :
-
Acceleration due to gravity
- G :
-
The shear moduli of rock
- h :
-
The distance between the slope top and the bottom of the tension crack
- H :
-
Slope height
- JCS:
-
The joint compressive strength
- JRC:
-
The joint roughness coefficient
- k h, k v :
-
Horizontal and vertical seismic acceleration coefficient
- k n,k s :
-
The normal and shear stiffness of the joints
- K :
-
The bulk moduli of rock
- l :
-
The distance between the slope top and the top of tension crack
- m(z),m B(z):
-
The mass of different elemental strip at depth z
- QAh,QAv:
-
Horizontal and vertical inertial force acting on block A
- Q Bh,Q Bv :
-
Horizontal and vertical inertial force acting on block B
- Z w :
-
Water level line height
- U A and U B :
-
Water pressure on the sliding surface of slider A and B
- V A and V B :
-
Water pressure on the cracked surface of slider A and B
- FSmw :
-
Minimum safety factor considering hydrostatic pressure
- Q h, Q v :
-
Horizontal and vertical inertial force acting on the whole slope
- t :
-
Time
- T :
-
Period of the harmonic and vertical seismic acceleration
- uh(z,t) and u v(z,t):
-
Horizontal and vertical displacement at any depth z and time t
- V s, V p :
-
Velocity of P - and S - waves in the rock
- W, W A,W B :
-
The weight of the rock slope, block A and block B respectively
- X :
-
Length of rock slope
- X A, X B :
-
Location of tension crack
- y 1,y 2 :
-
ks1H and ks1H
- z :
-
Depth from slope top
- α :
-
The slope face angle
- δ :
-
The dip of the tension crack
- γ :
-
The unit weight of rock
- ϕ :
-
The friction angle of rock
- ϕ r :
-
The residual friction angle
- θ :
-
The dip of the slope failure plane
- τ :
-
The shear stress of joint
- υ :
-
Poisson’s ratio
- ω :
-
Angular frequency of motion = 2π/T
- ξ Aand ξ B :
-
Xa/H and Xb/H
- ξ h :
-
h/H
- ξ 1 :
-
l/H
- γ w :
-
The severity of the water
- FSmin :
-
Minimum safety factor in the safety factor time history curves
- FSm :
-
Minimum safety factor without considering hydrostatic pressure
- σn :
-
The structural surface positive stress
- I F :
-
Interaction force between slider A and slider B
- x i and y i :
-
The x-coordinate value and y-coordinate value of the ith group of numbers
- f i :
-
Frequency of ith term
- a h,i(z,t),a v,i(z,t):
-
Horizontal and vertical acceleration at any depth z and time t for ith term
- φ b :
-
The basic friction angle of the structural surface
- ρ :
-
The Spearman correlation factor
- k i :
-
the Fourier factor of the ith term
- φ i :
-
Phase angle of ith term
- Q h,i(t), Q v,i(t):
-
Horizontal and vertical inertial force acting on the whole slope for ith term
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Acknowledgments
This study was financially supported by the National Natural Science Foundation of China (No. 51978666), the Hunan Province Science Fund for Distinguished Young Scholars (No. 2021JJ10063), the Scientific and Technological Progress and Innovation Project of Hunan Provincial Department of Transportation (No. 202115), the Fundamental Research Funds for the Central Universities of Central South University (NO. 2023ZZTS0677), the Natural Science Foundation of Hunan Province (NO. 2023JJ40078) and the Scientific Research Project of Hunan Provincial Education Department (No. 22C0573). All financial supports are greatly appreciated.
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All authors contributed to the study conception and design. Theoretical studies, numerical simulations, data collection and analysis were performed by ZHU Chen-hao, YU Cheng-hao and ZHAO Lian-heng. The first draft of the manuscript was written by ZHU Chen-hao and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Zhu, Ch., Zhao, Lh., Hu, Sh. et al. Seismic dynamic stability of double-slider rock slopes containing tension cracks. J. Mt. Sci. 20, 2093–2106 (2023). https://doi.org/10.1007/s11629-022-7855-y
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DOI: https://doi.org/10.1007/s11629-022-7855-y