Abstract
In rock slopes where sedimentary rock masses dip into the face of the slope, failure may occur by block toppling. In traditional analytical models, the failure surface is assumed to be a single plane running from the upper columns to the toe of the slopes, which may be inconsistent with the physical situation, where the weak plane has undergone counter-tilting within the rock slope due to variations of lithology and weak plane characteristics. To better reflect the physical situations, the failure surfaces ought to be determined instead of basing it on assumptions and incorporated in the existing analytical methods for stability analyses. Therefore, a searching technique for determining the counter-tilted failure surface angle has been proposed and traditional analytical models for evaluating the stability of rock slopes subjected to block toppling failure mechanisms have been modified by incorporating the counter-tilted weak plane angle. The physical slope with counter-tilted failure surface was comprehensively analyzed using the modified analytical model and the results were validated using numerical simulation models. The simulated failure mode zones are consistent with the failure mode zones obtained by the modified analytical method. The influence of relative angles of the counter-tilted failure surface on the slope stability has been studied and the results show that progressive increase of the counter-tilted failure surface angles lead to a gradual increase in slope instability. The proposed analytical method could provide precise applications to evaluate the slope instability in rock slopes with counter-tilted failure surface.
Similar content being viewed by others
References
Adhikary DP, Dyskin AV (2007) Modelling of progressive and instantaneous failures of foliated rock slopes. Rock Mech Rock Eng 40(4):349–362
Adhikary DP, Guo H (2002) An orthotropic Cosserat elasto-plastic model for layered rocks. Rock Mech Rock Eng 35(3):161–170
Adhikary DP, Dyskin AV, Jewell RJ (1995) Modelling of flexural toppling failures of rock slopes. In: Proceedings of the 8th international congress on rock mechanics, Tokyo, Japan, September 1995
Adhikary DP, Dyskin AV, Jewell RJ (1996) Numerical modelling of the flexural deformation of foliated rock slopes. Int J Rock Mech Min Sci Geomech Abstr 33(6):595–606
Adhikary DP, Dyskin AV, Jewell RJ, Stewart DP (1997) A study of the mechanism of flexural toppling failure of rock slopes. Rock Mech Rock Eng 30(2):75–93
Alejano LR, Gómez Márquez I, Pons B, Bastante FG, Alonso E (2006) Stability analysis of a potentially toppling over-tilted slope in granite. In: Proceedings of the 4th Asian rock mechanics symposium, Singapore, November 2006, pp 519–532
Alejano LR, Gómez-Márquez I, Martínez-Alegría R (2010) Analysis of a complex toppling-circular slope failure. Eng Geol 114(1–2):93–104
Alzo’ubi AK, Martin CD, Cruden DM (2010) Influence of tensile strength on toppling failure in centrifuge tests. Int J Rock Mech Min Sci 47:974–982
Amini M, Majdi A, Veshadi MA (2012) Stability analysis of rock slopes against block-flexure toppling failure. Rock Mech Rock Eng 45(4):519–532
Ashby J (1971) Sliding and toppling modes of failure in models and jointed rock slopes. MSc thesis, Imperial College, University of London
Aydan Ö, Kawamoto T (1992) The stability of slopes and underground openings against flexural toppling and their stabilisation. Rock Mech Rock Eng 25(3):143–165
Babiker AFA, Smith CC, Gilbert M, Ashby JP (2014) Non-associative limit analysis of the toppling-sliding failure of rock slopes. Int J Rock Mech Min Sci 71:1–11
Bobet A (1999) Analytical solutions for toppling failure. Int J Rock Mech Min Sci 36(7):971–980
Brideau MA, Stead D (2010) Controls on block toppling using a three-dimensional distinct element approach. Rock Mech Rock Eng 43:241–260
Cai JS (2013) Mechanism research of toppling deformation for homogeneous equal thickness anti-dip layered rock slopes. MSc thesis, China University of Geosciences, Beijing
Chen ZY, Gong WJ, Ma GW, Wang J, He L, Xing YC, Xing JY (2015) Comparisons between centrifuge and numerical modeling results for slope toppling failure. Chin J Technol Sci 58(9):1497–1508
Chen C, Zheng Y, Sun C (2016) An analytical approach on flexural toppling failure of counter-tilt slopes of layered rock. Chin J Rock Mech Eng 34:3505–3511
Cruden DM, Martin CD (2006) A century of risk management at the Frank Slide, Canada. The Geological Society of London, UK
De Freitas MH, Watters RJ (1973) Some field examples of toppling failure. Geotechnique 23:495–513
Gao L-T, Yan E-C, Xie L-F (2015) Improved Goodman–Bray method in consideration of groundwater effect. J Yangtse River Sci Res Inst 32(2):78
Goodman RE, Bray JW (1976) Toppling of rock slopes. In: Proceedings of the specialty conference on rock engineering for foundation and slopes, Boulder, Colorado, August 1976. American Society of Civil Engineering, New York, pp 201–234
Itasca Consulting Group, Inc. (2008) Three-dimensional distinct element code. Itasca Consulting Group, Inc., Minneapolis, MN
Lian JJ, Li Q, Deng XF, Zhao GF, Chen ZY (2017) A numerical study on toppling failure of a jointed rock slope by using the distinct lattice spring model. Rock Mech Rock Eng 51(2):513–530
Liu SC (2013) Study on toppling failure mechanism of rock slope in Rumei Hydropower Station. MSc thesis, China University of Geosciences, Beijing
Liu CH, Jaksa MB, Meyers AG (2008) Improved analytical solution for toppling stability analysis of rock slopes. Int J Rock Mech Min Sci 45(8):1361–1372
Liu CH, Jaksa MB, Meyers AG (2009) A transfer coefficient method for rock slope toppling. Can Geotech J 46(1):1–9
Liu CH, Jaksa MB, Meyers AG (2010) Toppling mechanisms of rock slopes considering stabilization from the underlying rock mass. Int J Rock Mech Min Sci 47(2):348–354
Majdi A, Amini M (2011) Analysis of geo-structural defects in flexural toppling failure. Int J Rock Mech Min Sci 48:175–186
Mohtarami E, Jafari A, Amini M (2014) Stability analysis of slopes against combined circular–toppling failure. Int J Rock Mech Min Sci 67:43-56
Pritchard MA, Savigny KW (1990) Numerical modelling of toppling. Can Geotech J 27:823–834
Pritchard MA, Savigny KW (1991) The Heather Hill landslide: an example of a large scale toppling failure in a natural slope. Can Geotech J 28:410–422
Ren G, Xia M, Li G, Liu C, Zhang F (2009) Study on toppling deformation and failure characteristics of steep bedding rock slope (in Chinese). Chin J Rock Mech Eng 28(1):193–3200
Sagaseta C, Sánchez JM, Cañizal J (2001) A general analytical solution for the required anchor force in rock slopes with toppling failure. Int J Rock Mech Min Sci 38(3):421–435
Scholtès L, Donzé F-V (2012) Modelling progressive failure in fractured rock masses using a 3D discrete element method. Int J Rock Mech Min Sci 52:18–30
Tatone BSA, Grasselli G (2010) ROCKTOPPLE: a spreadsheet-based program for probabilistic block-toppling analysis. Comput Geosci 36:98–114
Tan RJ, Yang XZ, Hu RL (2009) Review of deformation mechanism and stability analysis of anti-dipped rock slopes (in Chinese). Rock Soil Mech 30(Suppl 2):479–484
Wyllie DC (1999) Foundations on rock, 2nd edn. Taylor and Francis, London, UK, 401 pp
Wyllie DC, Mah CW (2004) Rock slope engineering: civil and mining. Taylor and Francis, London, UK
Yang B-J, He J, Ji G, Zhao T-H (2014) Stability analysis of sliding-toppling complex failure of rock slope (in Chinese). Rock Soil Mech 35(8):2335–2341
Zanbak C (1983) Design charts for rock slopes susceptible to toppling. J Geotech Eng 109(8):1039–1062
Zhang JH, Chen ZY, Wang XG (2007) Centrifuge modeling of rock slopes susceptible to block toppling. Rock Mech Rock Eng 40(4):363–382
Zhao GF (2015) Modelling 3D jointed rock masses using a lattice spring model. Int J Rock Mech Min Sci 78:79–90
Zhao GF (2017) Developing a four-dimensional lattice spring model for mechanical responses of solids. Comput Methods Appl Mech Eng 315:881–895
Zhao GF, Fang J, Zhao J (2011) A 3D distinct lattice spring model for elasticity and dynamic failure. Int J Numer Anal Methods Geomech 35:859–885
Zheng Y, Chen C, Liu X, Liu T, Zhou Y, Xia K, Fu H (2015a) Investigation on calculation method of layered counter-tilt slope for flexural toppling failure. Chin J Rock Mech Eng
Zheng Y, Chen CX, Liu TT, Liu XM, Song YF, Zhou YC (2015b) Analysis of toppling failure of rock slopes under the loads applied on the top. Rock Soil Mech 36:2639–2647
Zheng Y, Chen C, Liu T, Xia K, Liu X (2017) Stability analysis of rock slopes against sliding or flexural-toppling failure. Bull Eng Geol Environ, pp 1–21
Zuo BC, Chen CX, Liu XW, Shen Q (2005) Modeling experiment study on failure mechanism of counter-tilt rock slope. Chin J Rock Mech Eng 24:3505–3511
Acknowledgements
Special thanks go to the Natural Science Foundation of China for their financial support with project no. 51374163 and for the expertise and comments from the reviewers.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bowa, V.M., Xia, Y. Influence of counter-tilted failure surface angle on the stability of rock slopes subjected to block toppling failure mechanisms. Bull Eng Geol Environ 78, 2535–2550 (2019). https://doi.org/10.1007/s10064-018-1253-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10064-018-1253-2