Citation: | Linfeng Wang, Jixu Zhang, Wanchun Xia, Xiaoming Huang, Guojin Tan. Dynamic Stability and Fuzzy Reliability Analysis of Toppling Perilous Rock Under Seismic Excitation. Journal of Earth Science, 2024, 35(1): 248-262. doi: 10.1007/s12583-022-1740-z |
To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes, the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under the action of bidirectional earthquakes is proposed. First, the mass viscoelasticity model is used to simulate two main control surfaces of toppling perilous rock, the seismic dynamic response model and motion equation of toppling perilous rock are established based on the D'Alembert principle, and the Newmark-
Alfaro, P., Delgado, J., García-Tortosa, F. J., et al., 2012. The Role of Near-Field Interaction between Seismic Waves and Slope on the Triggering of a Rockslide at Lorca (SE Spain). Natural Hazards and Earth System Science, 12(167): 3631–3643. https://doi.org/10.5194/nhess-12-3631-2012 |
Ardestani, A., Amini, M., Esmaeili, K., 2021. A Two-Dimensional Limit Equilibrium Computer Code for Analysis of Complex Toppling Slope Failures. Journal of Rock Mechanics and Geotechnical Engineering, 13(1): 114–130. https://doi.org/10.1016/j.jrmge.2020.04.006 |
Che, A. L., Yang, H. K., Wang, B., et al., 2016. Wave Propagations through Jointed Rock Masses and Their Effects on the Stability of Slopes. Engineering Geology, 201: 45–56. https://doi.org/10.1016/j.enggeo. 2015.12.018 doi: 10.1016/j.enggeo.2015.12.018 |
Chen, H. K., Tang, H. M., Wang, R., 2004. Calculation Method of Stability for Unstable Rock and Application to the Three Gorges Reservoir. Chinese Journal of Rock Mechanics and Engineering, 23(4): 614–619 (in Chinese with English Abstract) |
Chen, H. K., Tang, H. M., Ye, S. Q., 2006. Damage Model of Control Fissure in Perilous Rock. Applied Mathematics and Mechanics (English Edition), 27(7): 967–974. https://doi.org/10.1007/s10483-006-0713-y |
Chen, X. L., Gao, R. X., Gong, W. H., et al., 2018. Random Seismic Response and Dynamic Fuzzy Reliability Analysis of Bedding Rock Slopes Based on Pseudoexcitation Method. International Journal of Geomechanics, 18(3): 04017165. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001084 |
Chen, Z. R., Song, D. Q., Liu, X. L., et al., 2022. Seismic Dynamic Response Characteristics of a Layered Slope at Tunnel Entrance Using Shaking Table Test. Earth Science, 47(6): 2069–2080 (in Chinese with English Abstract) |
Cheng, H. L., Zhou, J. M., Chen, Z. Y., et al., 2021. A Comparative Study of the Seismic Performances and Failure Mechanisms of Slopes Using Dynamic Centrifuge Modeling. Journal of Earth Science, 32(5): 1166–1173. https://doi.org/10.1007/s12583-021-1481-4 |
Dodagoudar, G. R., Venkatachalam, G., 2000. Reliability Analysis of Slopes Using Fuzzy Sets Theory. Computers and Geotechnics, 27(2): 101–115. https://doi.org/10.1016/S0266-352X(00)00009-4 |
Du, W. Q., 2018. Effects of Directionality and Vertical Component of Ground Motions on Seismic Slope Displacements in Newmark Sliding-Block Analysis. Engineering Geology, 239: 13–21. https://doi.org/10.1016/j.enggeo.2018.03.012 |
Ferrero, A. M., Migliazza, M. R., Pirulli, M., et al., 2016. Some Open Issues on Rockfall Hazard Analysis in Fractured Rock Mass: Problems and Prospects. Rock Mechanics and Rock Engineering, 49(9): 3615–3629. https://doi.org/10.1007/s00603-016-1004-2 |
Gao, L. G., Li, T. C., Liu, X. Q., et al., 2021. A Novel Dynamic Stability Analysis Method for Jointed Rock Slopes Based on Block-Interface Interaction. Computers and Geotechnics, 134: 104113. https://doi.org/10.1016/j.compgeo.2021.104113 |
Giasi, C. I., Masi, P., Cherubini, C., 2003. Probabilistic and Fuzzy Reliability Analysis of a Sample Slope near Aliano. Engineering Geology, 67(3/4): 391–402. https://doi.org/10.1016/S0013-7952(02)00222-3 |
Gong, J. X., 2003. Computational Methods for Reliability of Engineering Structures. Dalian University of Technology Press, Dalian (in Chinese) |
Huang, C., Wang, A. M., Ren, W. Z., 2010. Influence of Time Combination Pattern of Horizontal and Vertical Ground Motions on Slope Seismic Safety Factor. Rock and Soil Mechanics, 31(11): 3404–3410 (in Chinese with English Abstract) |
Huang, R. Q., Zhao, J. J., Ju, N. P., et al., 2013. Analysis of an Anti-Dip Landslide Triggered by the 2008 Wenchuan Earthquake in China. Natural Hazards, 68(2): 1021–1039. https://doi.org/10.1007/s11069-013-0671-5 |
Huang, Y., Xiong, M., 2017. Dynamic Reliability Analysis of Slopes Based on the Probability Density Evolution Method. Soil Dynamics and Earthquake Engineering, 94: 1–6. https://doi.org/10.1016/j.soildyn. 2016.11.011 doi: 10.1016/j.soildyn.2016.11.011 |
Huang, Y., Xiong, M., Zhou, H. B., 2015. Ground Seismic Response Analysis Based on the Probability Density Evolution Method. Engineering Geology, 198: 30–39. https://doi.org/10.1016/j.enggeo. 2015.09.004 doi: 10.1016/j.enggeo.2015.09.004 |
Juang, C. H., Jhi, Y. Y., Lee, D. H., 1998. Stability Analysis of Existing Slopes Considering Uncertainty. Engineering Geology, 49(2): 111–122. https://doi.org/10.1016/S0013-7952(97)00078-1 |
Koç, M. L., Balas, C. E., 2013. Reliability Analysis of a Rubble Mound Breakwater Using the Theory of Fuzzy Random Variables. Applied Ocean Research, 39: 83–88. https://doi.org/10.1016/j.apor.2012.10.007 |
Korzec, A., Jankowski, R., 2021. Extended Newmark Method to Assess Stability of Slope under Bidirectional Seismic Loading. Soil Dynamics and Earthquake Engineering, 143: 106600. https://doi.org/10.1016/j.soildyn.2021.106600 |
Kulatilake, P. H. S. W., Shreedharan, S., Sherizadeh, T., et al., 2016. Laboratory Estimation of Rock Joint Stiffness and Frictional Parameters. Geotechnical and Geological Engineering, 34(6): 1723–1735. https://doi.org/10.1007/s10706-016-9984-y |
Lei, H., Wang, X. L., Hou, H., et al., 2018. The Earthquake in Jiuzhaigou County of Northern Sichuan, China on August 8, 2017. Natural Hazards, 90(2): 1021–1030. https://doi.org/10.1007/s11069-017-3064-3 |
Li, X. L., Li, Z. Q., Yang, J. S., et al., 2020. Seismic Vulnerability Comparison between Rural Weinan and Other Rural Areas in Western China. International Journal of Disaster Risk Reduction, 48: 101576. https://doi.org/10.1016/j.ijdrr.2020.101576 |
Liu, H. L., Fei, K., Gao, Y. F., 2003. Time History Analysis Method of Slope Seismic Stability. Rock and Soil Mechanics, 24(4): 553–556 (in Chinese with English Abstract) |
Liu, J. B., Du, X. L., 2005. Dynamics of Structures. China Machine Press, Beijing (in Chinese) |
Liu, X. R., Liu, Y. Q., He, C. M., et al., 2018. Dynamic Stability Analysis of the Bedding Rock Slope Considering the Vibration Deterioration Effect of the Structural Plane. Bulletin of Engineering Geology and the Environment, 77(1): 87–103. https://doi.org/10.1007/s10064-016-0945-8 |
Luo, G., Cheng, Q. G., Shen, W. G., et al., 2022. Research Status and Development Trend of the High-Altitude Extremely-Energetic Rockfalls. Earth Science, 47(3): 913–934 (in Chinese with English Abstract) |
Maghous, S., Bernaud, D., Fréard, J., et al., 2008. Elastoplastic Behavior of Jointed Rock Masses as Homogenized Media and Finite Element Analysis. International Journal of Rock Mechanics and Mining Sciences, 45(8): 1273–1286. https://doi.org/10.1016/j.ijrmms. 2008.01.008 doi: 10.1016/j.ijrmms.2008.01.008 |
Newmark, N. M., 1965. Effects of Earthquakes on Dams and Embankments. Géotechnique, 15(2): 139–160. https://doi.org/10.1680/geot.1965.15.2.139 |
Pang, R., Xu, B., Zhou, Y., et al., 2021. Seismic Time-History Response and System Reliability Analysis of Slopes Considering Uncertainty of Multi-Parameters and Earthquake Excitations. Computers and Geotechnics, 136: 104245. https://doi.org/10.1016/j.compgeo. 2021.104245 doi: 10.1016/j.compgeo.2021.104245 |
Park, H. J., Um, J. G., Woo, I., et al., 2012. Application of Fuzzy Set Theory to Evaluate the Probability of Failure in Rock Slopes. Engineering Geology, 125: 92–101. https://doi.org/10.1016/j.enggeo.2011.11.008 |
Park, H. J., West, T. R., Woo, I., 2005. Probabilistic Analysis of Rock Slope Stability and Random Properties of Discontinuity Parameters, Interstate Highway 40, Western North Carolina, USA. Engineering Geology, 79(3/4): 230–250. https://doi.org/10.1016/j.enggeo. 2005.02.001 doi: 10.1016/j.enggeo.2005.02.001 |
Pathak, S., Nilsen, B., 2004. Probabilistic Rock Slope Stability Analysis for Himalayan Conditions. Bulletin of Engineering Geology and the Environment, 63(1): 25–32. https://doi.org/10.1007/s10064-003-0226-1 |
San, K. C., Leshchinsky, D., 1994. Seismic Slope Stability Analysis: Pseudo-Static Generalized Method. Soils and Foundations, 34(2): 73–77. https://doi.org/10.3208/sandf1972.34.2_73 |
Song, D. Q., Chen, Z., Dong, L. H., et al., 2021. Investigation of the Seismic Response Characteristics of a Rock Mass Slope Containing Weak Structural Planes under Seismic Excitation Based on Multi-Domain Coupling Analysis. Geomatics, Natural Hazards and Risk, 12(1): 2776–2802. https://doi.org/10.1080/19475705.2021.1975834 |
Song, D. Q., Chen, Z., Ke, Y. T., et al., 2020a. Seismic Response Analysis of a Bedding Rock Slope Based on the Time-Frequency Joint Analysis Method: A Case Study from the Middle Reach of the Jinsha River, China. Engineering Geology, 274: 105731. https://doi.org/10.1016/j.enggeo.2020.105731 |
Song, D. Q., Chen, Z., Chao, H., et al., 2020b. Numerical Study on Seismic Response of a Rock Slope with Discontinuities Based on the Time-Frequency Joint Analysis Method. Soil Dynamics and Earthquake Engineering, 133: 106112. https://doi.org/10.1016/j.soildyn. 2020.106112 doi: 10.1016/j.soildyn.2020.106112 |
Strenk, P. M., Wartman, J., 2011. Uncertainty in Seismic Slope Deformation Model Predictions. Engineering Geology, 122(1/2): 61–72. https://doi.org/10.1016/j.enggeo.2011.03.003 |
Wang, G. Y., Han, Y., 2012. Fuzzy Reliability Analysis of Geocell Protective Slope Stability. Applied Mechanics and Materials, 166/167/168/169: 1917–1921. https://doi.org/10.4028/www.scientific.net/amm.166-169.1917 |
Wang, L. Q., Yin, Y. P., Huang, B. L., et al., 2020. Damage Evolution and Stability Analysis of the Jianchuandong Dangerous Rock Mass in the Three Gorges Reservoir Area. Engineering Geology, 265: 105439. https://doi.org/10.1016/j.enggeo.2019.105439 |
Wang, Y., Song, X. L., Zhang, H., et al., 2011. Fuzzy Stochastic Reliability Analysis of Slope Engineering. Journal of Yangtze River Scientific Research Institute, 28(9): 30–34. https://doi.org/10.1007/s12583-011-0163-z (in Chinese with English Abstract) |
Wang, Y. J., 2017. A Novel Story on Rock Slope Reliability, by an Initiative Model that Incorporated the Harmony of Damage, Probability and Fuzziness. Geomechanics and Engineering, 12(2): 269–294. https://doi.org/10.12989/gae.2017.12.2.269 |
Xia, P., Hu, X. L., Wu, S. S., et al., 2020. Slope Stability Analysis Based on Group Decision Theory and Fuzzy Comprehensive Evaluation. Journal of Earth Science, 31(6): 1121–1132. https://doi.org/10.1007/s12583-020-1101-8 |
Xiong, M., Huang, Y., 2017. Stochastic Seismic Response and Dynamic Reliability Analysis of Slopes: A Review. Soil Dynamics and Earthquake Engineering, 100: 458–464. https://doi.org/10.1016/j.soildyn.2017.06.017 |
Yin, Y. P., Huang, B. L., Liu, G. N., et al., 2015. Potential Risk Analysis on a Jianchuandong Dangerous Rockmass-Generated Impulse Wave in the Three Gorges Reservoir, China. Environmental Earth Sciences, 74(3): 2595–2607. https://doi.org/10.1007/s12665-015-4278-x |
Yin, Y. P., Wang, F. W., Sun, P., 2009. Landslide Hazards Triggered by the 2008 Wenchuan Earthquake, Sichuan, China. Landslides, 6(2): 139–152. https://doi.org/10.1007/s10346-009-0148-5 |
Zeng, T. R., Jiang, H. W., Liu, Q. L., et al., 2022a. Landslide Displacement Prediction Based on Variational Mode Decomposition and MIC-GWO-LSTM Model. Stochastic Environmental Research and Risk Assessment, 36(5): 1353–1372. https://doi.org/10.1007/s00477-021-02145-3 |
Zeng, T. R., Yin, K. L., Jiang, H. W., et al., 2022b. Groundwater Level Prediction Based on a Combined Intelligence Method for the Sifangbei Landslide in the Three Gorges Reservoir Area. Scientific Reports, 12(1): 11108. https://doi.org/10.1038/s41598-022-14037-9 |
Zhang, L. L., Zhang, J., Xu, Y., et al., 2011. Reliability Theory of Geotechnical Engineering. Tongji University Press, Shanghai (in Chinese) |
Zhang, M., 2009. Structural Reliability Analysis—Methods and Procedures. Science Press, Beijing (in Chinese) |
Zhang, W. G., Meng, F. S., Chen, F. Y., et al., 2021. Effects of Spatial Variability of Weak Layer and Seismic Randomness on Rock Slope Stability and Reliability Analysis. Soil Dynamics and Earthquake Engineering, 146: 106735.https://doi.org/10.1016/j.soildyn. 2021.106735 doi: 10.1016/j.soildyn.2021.106735 |
Zhao, L. H., Cheng, X., Dan, H. C., et al., 2017. Effect of the Vertical Earthquake Component on Permanent Seismic Displacement of Soil Slopes Based on the Nonlinear Mohr-Coulomb Failure Criterion. Soils and Foundations, 57(2): 237–251.https://doi.org/10.1016/j.sandf. 2016.12.002 doi: 10.1016/j.sandf.2016.12.002 |