Advanced Search

Indexed by SCI、CA、РЖ、PA、CSA、ZR、etc .

Volume 35 Issue 4
Aug 2024
Turn off MathJax
Article Contents
Jiongchao Wang, Jun Zheng, Jichao Guo, Qing Lü, Jianhui Deng. A Method for Evaluating the Maximum Bending Degree of Flexural Toppling Rock Masses Based on the Rock Tensile Strain-Softening Model. Journal of Earth Science, 2024, 35(4): 1243-1253. doi: 10.1007/s12583-022-1805-z
Citation: Jiongchao Wang, Jun Zheng, Jichao Guo, Qing Lü, Jianhui Deng. A Method for Evaluating the Maximum Bending Degree of Flexural Toppling Rock Masses Based on the Rock Tensile Strain-Softening Model. Journal of Earth Science, 2024, 35(4): 1243-1253. doi: 10.1007/s12583-022-1805-z

A Method for Evaluating the Maximum Bending Degree of Flexural Toppling Rock Masses Based on the Rock Tensile Strain-Softening Model

doi: 10.1007/s12583-022-1805-z
More Information
  • Corresponding author: Jun Zheng, zhengjun12@zju.edu.cn
  • Received Date: 30 May 2022
  • Accepted Date: 25 Dec 2022
  • Available Online: 16 Aug 2024
  • Issue Publish Date: 30 Aug 2024
  • Flexural toppling occurs when a series of layered rock masses bend towards their free face. It is important to evaluate the maximum bending degree and the requirement of supports of flexural toppling rock mass to prevent rock mass cracking and even failure leading to a landslide. Based on the rock tensile strain-softening model, this study proposes a method for calculating the maximum curvature (Cppmax) of flexural toppling rock masses. By applying this method to calculate Cppmax of 9 types of rock masses with different hardness and rock layer thickness, some conclusions are drawn: (1) the internal key factors affecting Cppmax are E* (E*= Ess/E0, where E0 and Ess are the mean deformation moduli of the rock before and after reaching its peak tensile strength, respectively), the strain εt corresponding to the tensile strength of rock, and the thickness (h) of rock layers; (2) hard rock layers are more likely to develop into block toppling than soft rock layers; and (3) thin rock layers are more likely to remain in flexural toppling state than thick rock layers. In addition, it is found that Cppmax for flexural toppling rock masses composed of bedded rocks such as gneiss is related to the tensile direction.

     

  • Conflict of Interest
    The authors declare that they have no conflict of interest.
  • loading
  • Adhikary, D. P., Dyskin, A. V., Jewell, R. J., et al., 1997. A Study of the Mechanism of Flexural Toppling Failure of Rock Slopes. Rock Mechanics and Rock Engineering, 30(2): 75–93. https://doi.org/10.1007/BF01020126
    Alejano, L. R., Alonso, E., Rodríguez-Dono, A., et al., 2010. Application of the Convergence-Confinement Method to Tunnels in Rock Masses Exhibiting Hoek-Brown Strain-Softening Behaviour. International Journal of Rock Mechanics and Mining Sciences, 47(1): 150–160. https://doi.org/10.1016/j.ijrmms.2009.07.008
    Alejano, L. R., Carranza-Torres, C., Giani, G. P., et al., 2015. Study of the Stability Against Toppling of Rock Blocks with Rounded Edges Based on Analytical and Experimental Approaches. Engineering Geology, 195: 172–184. https://doi.org/10.1016/j.enggeo.2015.05.030
    Alejano, L. R., Sánchez-Alonso, C., Pérez-Rey, I., et al., 2018. Block Toppling Stability in the Case of Rock Blocks with Rounded Edges. Engineering Geology, 234: 192–203. https://doi.org/10.1016/j.enggeo.2018.01.010
    Alonso, E., Alejano, L. R., Varas, F., et al., 2003. Ground Response Curves for Rock Masses Exhibiting Strain-Softening Behaviour. International Journal for Numerical and Analytical Methods in Geomechanics, 27(13): 1153–1185. https://doi.org/10.1002/nag.315
    Alzo'ubi, A. K., Martin, C. D., Cruden, D. M., 2010. Influence of Tensile Strength on Toppling Failure in Centrifuge Tests. International Journal of Rock Mechanics and Mining Sciences, 47(6): 974–982. https://doi.org/10.1016/j.ijrmms.2010.05.011
    Amini, M., Majdi, A., Aydan, Ö., 2009. Stability Analysis and the Stabilisation of Flexural Toppling Failure. Rock Mechanics and Rock Engineering, 42(5): 751–782. https://doi.org/10.1007/s00603-008-0020-2
    Amini, M., Majdi, A., Veshadi, M. A., 2012. Stability Analysis of Rock Slopes Against Block-Flexure Toppling Failure. Rock Mechanics and Rock Engineering, 45(4): 519–532. https://doi.org/10.1007/s00603-012-0220-7
    Aydan, Ö., Kawamoto, T., 1992. The Stability of Slopes and Underground Openings Against Flexural Toppling and Their Stabilisation. Rock Mechanics and Rock Engineering, 25(3): 143–165. https://doi.org/10.1007/BF01019709
    Bowa, V. M., Xia, Y. Y., 2018. Modified Analytical Technique for Block Toppling Failure of Rock Slopes with Counter-Tilted Failure Surface. Indian Geotechnical Journal, 48(4): 713–727. https://doi.org/10.1007/s40098-018-0303-9
    Brideau, M. A., Stead, D., 2010. Controls on Block Toppling Using a Three-Dimensional Distinct Element Approach. Rock Mechanics and Rock Engineering, 43(3): 241–260. https://doi.org/10.1007/s00603-009-0052-2
    Cadoni, E., 2010. Dynamic Characterization of Orthogneiss Rock Subjected to Intermediate and High Strain Rates in Tension. Rock Mechanics and Rock Engineering, 43(6): 667–676. https://doi.org/10.1007/s00603-010-0101-x
    Cai, J. C., Ju, N. P., Huang, R. Q., et al., 2019. Mechanism of Toppling and Deformation in Hard Rock Slope: A Case of Bank Slope of Hydropower Station, Qinghai Province, China. Journal of Mountain Science, 16(4): 924–934. https://doi.org/10.1007/s11629-018-5096-x
    Chen, Z. Y., Gong, W. J., Ma, G. W., et al., 2015. Comparisons between Centrifuge and Numerical Modeling Results for Slope Toppling Failure. Science China Technological Sciences, 58(9): 1497–1508. https://doi.org/10.1007/s11431-015-5889-x
    Chuang, T. J., Mai, Y. W., 1989. Flexural Behavior of Strain-Softening Solids. International Journal of Solids and Structures, 25(12): 1427–1443. https://doi.org/10.1016/0020-7683(89)90110-8
    Cruden, D. M., Hu, X. Q., 1994. Topples on Underdip Slopes in the Highwood Pass, Alberta, Canada. Quarterly Journal of Engineering Geology, 27(1): 57–68. https://doi.org/10.1144/gsl.qjegh.1994.027.p1.08
    Goodman, R. E., Bray, J. W., 1977. Toppling of Rock Slopes. 2: 201–234
    Guo, J. C., Zheng, J., Lü, Q., et al., 2022. Estimation of Fracture Size and Azimuth in the Universal Elliptical Disc Model Based on Trace Information. Journal of Rock Mechanics and Geotechnical Engineering, https://doi.org/10.1016/j.jrmge.2022.07.018
    Hoek, E., Brown, E. T., 1997. Practical Estimates of Rock Mass Strength. International Journal of Rock Mechanics and Mining Sciences, 34(8): 1165–1186. https://doi.org/10.1016/S1365-1609(97)80069-X
    Huang, R. Q., 2012. Mechanisms of Large-Scale Landslides in China. Bulletin of Engineering Geology and the Environment, 71(1): 161–170. https://doi.org/10.1007/s10064-011-0403-6
    Hudson, J. A., Crouch, S. L., Fairhurst, C., 1972. Soft, Stiff and Servo-Controlled Testing Machines: A Review with Reference to Rock Failure. Engineering Geology, 6(3): 155–189. https://doi.org/10.1016/0013-7952(72)90001-4
    Katsunori, F., Fengnian, J., Seisuke, O., 1995. Complete Stress-Strain Curves of Rock in Uniaxial Tension Test. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 11(1): 25–29. https://doi.org/10.2473/shigentosozai.111.25
    Kiliç, R., Ulamiş, K., 2020. Toppling and Sliding in Volcanic Bimrocks around Bayrakli (Izmir, Turkey). Journal of Mountain Science, 17(2): 492–500. https://doi.org/10.1007/s11629-019-5648-8
    Lanaro, F., Jing, L., Stephansson, O., et al., 1997. D. E. M. Modelling of Laboratory Tests of Block Toppling. International Journal of Rock Mechanics and Mining Sciences, 34(3/4): 173.e1–173.e15. https://doi.org/10.1016/S1365-1609(97)00116-0
    Li, A., Dai, F., Liu, Y., et al., 2021. Dynamic Stability Evaluation of Underground Cavern Sidewalls Against Flexural Toppling Considering Excavation-Induced Damage. Tunnelling and Underground Space Technology, 112: 103903. https://doi.org/10.1016/j.tust.2021.103903
    Li, A., Dai, F., Xu, N. W., et al., 2019. Analysis of a Complex Flexural Toppling Failure of Large Underground Caverns in Layered Rock Masses. Rock Mechanics and Rock Engineering, 52(9): 3157–3181. https://doi.org/10.1007/s00603-019-01760-5
    Li, L., Liu, J., Cui, W., et al., 2012. Discontinuous Toppling Characteristics of a Retrograde Layered Rock Slope in the Upper Reaches of the Yellow River. Gansu Water Resources and Hydropower Technology, 54(12): 36–40. https://doi.org/10.19645/j.issn2095-0144.2018.12.011 (in Chinese)
    Li, Z., Wang, J. A., Li, L., et al., 2015. A Case Study Integrating Numerical Simulation and GB-InSAR Monitoring to Analyze Flexural Toppling of an Anti-Dip Slope in Fushun Open Pit. Engineering Geology, 197: 20–32. https://doi.org/10.1016/j.enggeo.2015.08.012
    Liu, C. H., Jaksa, M. B., Meyers, A. G., 2010. Toppling Mechanisms of Rock Slopes Considering Stabilization from the Underlying Rock Mass. International Journal of Rock Mechanics and Mining Sciences, 47(2): 348–354. https://doi.org/10.1016/j.ijrmms.2009.11.008
    Liu, F. Z., 1996. Study on Mechanical Property of Rock in Tension and Tension Shear State. Journal of Yangtze River Scientific Research Institute, 13(3): 35–39 (in Chinese with English Abstract)
    Liu, H., Zhao, Y., Dong, J., et al., 2022. Seismic Dynamic Response and Failure Mode of Anti-Dip Rock Slope with Weak Rock Stratum. Earth Science, 47(12): 4373–4389. https://doi.org/10.3799/dqkx.2022.355 (in Chinese with English Abstract)
    Liu, J., Xu, J., Yang, C., et al., 2011. Mechanical Characteristics of Tensile Failure of Salt Rock. Chinese Journal of Geotechnical Engineering, 33(4): 580–586 (in Chinese with English Abstract)
    Liu, Y., 2019. Stability Analysis and Harnessing of the Landslides at No. 3 Branch Opening in Qinling Tunnel. Engineering Construction, 51(1): 45–50. https://doi.org/10.13402/j.gcjs.2019.01.009 (in Chinese with English Abstract)
    Meda, A., 2003. Tensile Behaviour in Natural Building Stone: Serena Sandstone. Materials and Structures, 36(8): 553–559. https://doi.org/10.1007/BF02480833
    Ministry of Construction (PRCMC), 2002. GB50021-2001, Code for Investigation of Geotechnical Engineering. 3: 6–10
    Nichol, S. L., 2000. Examination of Toppling Behaviour in Large Rock Slopes Using the UDEC Computer Code. 1–146
    Nichol, S. L., Hungr, O., Evans, S. G., 2002. Large-Scale Brittle and Ductile Toppling of Rock Slopes. Canadian Geotechnical Journal, 39(4): 773–788. https://doi.org/10.1139/t02-027
    Ning, Y. B., Zhang, G. C., Tang, H. M., et al., 2019. Process Analysis of Toppling Failure on Anti-Dip Rock Slopes under Seismic Load in Southwest China. Rock Mechanics and Rock Engineering, 52(11): 4439–4455. https://doi.org/10.1007/s00603-019-01855-z
    Nonomura, A., Hasegawa, S., 2013. Regional Extraction of Flexural-Toppled Slopes in Epicentral Regions of Subduction Earthquakes along the Nankai Trough Using DEMs. Environmental Earth Sciences, 68(1): 139–149. https://doi.org/10.1007/s12665-012-1722-z
    Parent, P., Zucker, S. W., 1989. Trace Inference, Curvature Consistency, and Curve Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(8): 823–839. https://doi.org/10.1109/34.31445
    Park, K. H., Tontavanich, B., Lee, J. G., 2008. A Simple Procedure for Ground Response Curve of Circular Tunnel in Elastic-Strain Softening Rock Masses. Tunnelling and Underground Space Technology, 23(2): 151–159. https://doi.org/10.1016/j.tust.2007.03.002
    Regmi, A. D., Yoshida, K., Nagata, H., et al., 2014. Rock Toppling Assessment at Mugling-Narayanghat Road Section: 'A Case Study from Mauri Khola Landslide', Nepal. CATENA, 114: 67–77. https://doi.org/10.1016/j.catena.2013.10.013
    Smith, J. V., 2015. Self-Stabilization of Toppling and Hillside Creep in Layered Rocks. Engineering Geology, 196: 139–149. https://doi.org/10.1016/j.enggeo.2015.07.008
    Wang, F., Li, J., Ma, B., et al., 2010. Classification System and Type Distribution of Rock in Highway Rock and Soil Zoning. Journal of Highway and Transportation Research and Development, 27(6): 102–106 (in Chinese with English Abstract)
    Wang, X. B., 2006. Unified Analytical Stress—Strain Curve for Quasibrittle Geomaterial in Uniaxial Tension, Direct Shear and Uniaxial Compression. Journal of Central South University of Technology, 13(1): 99–104. https://doi.org/10.1007/s11771-006-0114-5
    Wang, X. B., 2007. Distributions of Local Damage Variable and Local Plastic Tensile Strain and Precursors to Failure of Quasi-Brittle Pure Bending Beam. Key Engineering Materials, 347: 447–452. https://doi.org/10.4028/www.scientific.net/kem.347.447
    Wei, W., Duan, S., Jiang, Q., et al., 2008. Research on Some Factors Influencing the Toppling Stability in Anti-Inclined Slope. Rock and Soil Mechanics, 29(S1): 431–434 (in Chinese with English Abstract)
    Wu, X., Yang, P., Chen, J., 2018. The Strain Softening Model of Rock Damage under Compression and Tension. International Journal for Engineering Modelling, 31(3): 67–77. https://doi.org/10.31534/engmod.2018.3.ri.05m
    Xiang, Y., Jiao, Y. Q., Wu, L. Q., et al., 2022. Markers and Genetic Mechanisms of Primary and Epigenetic Oxidation of an Aeolian Depositional System of the Luohandong Formation, Ordos Basin. Journal of Earth Science, 33(2): 358–372. https://doi.org/10.1007/s12583-020-1109-0
    Xu, B., Liu, X., 1995. Applied Elastoplastic Mechanics. Tsinghua University Press, Beijing (in Chinese)
    Yang, C. H., Daemen, J. J. K., Yin, J. H., 1999. Experimental Investigation of Creep Behavior of Salt Rock. International Journal of Rock Mechanics and Mining Sciences, 36(2): 233–242. https://doi.org/10.1016/S0148-9062(98)00187-9
    Yang, J. L., Wang, C., Jin, Z. M., 2022. Crystallization of Hydrous Ti-Rich Basaltic Magma and Its Implication for the Origin of Fe–Ti Oxide in Layered Intrusions of the Emeishan Large Igneous Province. Journal of Earth Science, 33(2): 507–512. https://doi.org/10.1007/s12583-021-1475-2
    Zeng, L. B., Ma, S. J., Tian, H., et al., 2022. Research Progress of Natural Fractures in Organic Rich Shale. Earth Science. https://doi.org/10.3799/dqkx.2022.190 (in Chinese with English Abstract)
    Zhang, J. H., Chen, Z. Y., Wang, X. G., 2007. Centrifuge Modeling of Rock Slopes Susceptible to Block Toppling. Rock Mechanics and Rock Engineering, 40(4): 363–382. https://doi.org/10.1007/s00603-006-0112-9
    Zheng, D., Wang, Q., Man, F., 2019. Centrifuge Model Test Study on Key Hazard Inducing Factors of Deep Toppling Deformation and Disaster Patterns of Counter-Tilt Layered Rock Slopes. Chinese Journal of Rock Mechanics and Engineering, 38(10): 1954–1963 (in Chinese with English Abstract)
    Zheng, J., Guo, J. C., Wang, J. C., et al., 2022. A Universal Elliptical Disc (UED) Model to Represent Natural Rock Fractures. International Journal of Mining Science and Technology, 32(2): 261–270. https://doi.org/10.1016/j.ijmst.2021.12.001
    Zheng, J., Lü, Q., Deng, J. H., et al., 2019. A Modified Stereographic Projection Approach and a Free Software Tool for Kinematic Analysis of Rock Slope Toppling Failures. Bulletin of Engineering Geology and the Environment, 78(7): 4757–4769. https://doi.org/10.1007/s10064-018-1426-z
    Zheng, J., Wang, X. H., Lü, Q., et al., 2020. A Contribution to Relationship between Volumetric Joint Count (Jv) and Rock Quality Designation (RQD) in Three-Dimensional (3-D) Space. Rock Mechanics and Rock Engineering, 53(3): 1485–1494. https://doi.org/10.1007/s00603-019-01986-3
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(12)  / Tables(4)

    Article Metrics

    Article views(60) PDF downloads(105) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return