Numerical Study on Dynamic Response of a Horizontal Layered-Structure Rock Slope under a Normally Incident Sv Wave
Abstract
:1. Introduction
2. Validation of FLAC Modeling on Wave Transmission across Rock Joints
2.1. Normally Incident P Wave Transmission through a Single Joint
2.2. Normally Incident SV Wave Transmission through a Single Joint
2.3. Normally Incident P Wave Transmission through a Joint Set
2.4. Obliquely Incident P Wave Transmission through a Single Joint
3. Dynamic Response Analysis Method
3.1. Computational Model
3.2. Model Properties
4. Parametric Studies on Sv Wave Transmission through the Horizontal Layered-Structure Rock Slope
4.1. Parametric Study on Normalized Fracture Stiffness K
4.2. Parametric Study on Dimensionless Fracture Spacing ξ
5. Discussion of Results
6. Conclusions
- The acceleration amplification coefficient η decreases with the increase of the normalized fracture stiffness K, and the decrease rate is obviously reduced once K is larger than 2;
- The acceleration amplification coefficient η does not increase with the increase of the dimensionless fracture spacing ξ, and there is a decrease range due to the superposition of the reflection and the refraction from the joints;
- The effect of the dimensionless fracture spacing ξ is more obvious on the acceleration amplification coefficient η than that of the normalized fracture stiffness K.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Density (kg/m³) | Bulk Modulus (GPa) | Shear Modulus (GPa) |
---|---|---|
2570 | 13.44 | 10.08 |
Density (kg/m³) | Bulk Modulus (GPa) | Shear Modulus (GPa) |
---|---|---|
2500 | 27.8 | 20.8 |
Parameters | Value | ||||||||
---|---|---|---|---|---|---|---|---|---|
ξ | 0.01 | 0.0125 | 0.02 | 0.05 | 0.1 | 0.2 | 0.3 | 0.4 | |
f (s−1) | 2.89 | 3.61 | 5.77 | 14.44 | 28.87 | 57.74 | 86.61 | 115.48 | |
K = 0.1 | k (Pa/m) | 1.31 × 107 | 1.64 × 107 | 2.62 × 107 | 6.55 × 107 | 1.31 × 108 | 2.62 × 108 | 3.93 × 108 | 5.24 × 108 |
K = 0.25 | 3.275 × 107 | 4.1 × 107 | 6.55 × 107 | 1.638 × 108 | 3.275 × 108 | 6.55 × 108 | 9.825 × 108 | 1.31 × 109 | |
K = 0.5 | 6.55 × 107 | 8.2 × 107 | 1.31 × 108 | 3.275 × 108 | 6.55 × 108 | 1.31 × 109 | 1.965 × 109 | 2.62 × 109 | |
K = 1 | 1.31 × 108 | 1.64 × 108 | 2.62 × 108 | 6.55 × 108 | 1.31 × 109 | 2.62 × 109 | 3.93 × 109 | 5.24 × 109 | |
K = 2 | 2.62 × 108 | 3.28 × 108 | 5.24 × 108 | 1.31 × 109 | 2.62 × 109 | 5.24 × 109 | 7.86 × 109 | 1.048 × 1010 | |
K = 3 | 3.93 × 108 | 4.92 × 108 | 7.86 × 108 | 1.97 × 109 | 3.93 × 109 | 7.86 × 109 | 1.179 × 1010 | 1.572 × 1010 | |
K = 4 | 5.24 × 108 | 6.56 × 108 | 1.05 × 109 | 2.62 × 109 | 5.24 × 109 | 1.05 × 1010 | 1.572 × 1010 | 2.096 × 1010 | |
K = 5 | 6.55 × 108 | 8.20 × 108 | 1.31 × 109 | 3.28 × 109 | 6.55 × 109 | 1.31 × 1010 | 1.965 × 1010 | 2.62 × 1010 | |
σS (Pa) | 3.98 × 106 | 3.18 × 106 | 1.99 × 106 | 7.93 × 105 | 4.02 × 105 | 1.95 × 105 | 1.376 × 105 | 1.032 × 105 |
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Zhan, Z.; Qi, S. Numerical Study on Dynamic Response of a Horizontal Layered-Structure Rock Slope under a Normally Incident Sv Wave. Appl. Sci. 2017, 7, 716. https://doi.org/10.3390/app7070716
Zhan Z, Qi S. Numerical Study on Dynamic Response of a Horizontal Layered-Structure Rock Slope under a Normally Incident Sv Wave. Applied Sciences. 2017; 7(7):716. https://doi.org/10.3390/app7070716
Chicago/Turabian StyleZhan, Zhifa, and Shengwen Qi. 2017. "Numerical Study on Dynamic Response of a Horizontal Layered-Structure Rock Slope under a Normally Incident Sv Wave" Applied Sciences 7, no. 7: 716. https://doi.org/10.3390/app7070716