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A General Solution for Estimating the Safety Factor of Bimslopes

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Bimslopes are slopes underlain by block-in-matrix rocks/soils (bimrocks/bimsoils), which are heterogeneous geomaterials with complex behavior. Abundant uncertainties in the mechanical, spatial, and geological nature of bimslopes make it difficult to estimate stability conditions of bimslopes. In this paper, some factors affecting the stability of bimslopes are investigated using the finite-element method. The main contributory factors include Volumetric Block Proportion (VBP), the inclination of blocks, and the strength of matrix/block interfaces. By performance of sensitivity analysis on these factors, a statistically significant equation was obtained to estimate the safety factor of bimslopes using the multivariate regression method. The influence of block configurations and groundwater levels on the stability of bimslopes was then investigated to more confidently use the multivariate equation. Finally, to check the validity of procedures presented in this paper, a real failed bimslope in the Sungun mine (Iran) was investigated. The acceptable results from the Sungun analysis demonstrated the safety factor of bimslopes can be estimated using the practical solution presented in this paper.


  • Development of more than 1300 numerical models to analyze the key factors affecting the stability of block-in-matrix slopes (bimslopes).

  • Investigation of the influence of volumetric block proportion, the inclination of blocks, and strength of matrix/block interface on the safety factor of bimslopes.

  • Consideration of the substantial uncertainties affecting the analysis of bimslopes.

  • Presentation of the results of research in the form of applied schemes and tables.

  • Provision of a practical procedure and equation for estimating the safety factor of bimslopes.

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Data Availability

The analyzed data were obtained through modeling done by the authors, and the data of the case study were obtained from field mapping and a related report from the Sungun mine.


  • Brown CE (1998) Coefficient of variation. Applied multivariate statistics in geohydrology and related sciences. Springer, Berlin, pp 155–157

    Chapter  Google Scholar 

  • Cen D, Huang D, Ren F (2017) Shear deformation and strength of the interphase between the soil–rock mixture and the benched bedrock slope surface. Acta Geotech 12:391–413.

    Article  Google Scholar 

  • Coli M, Tanzini M (2013) Characterization of the “chaotic complex”(Northern Apennines, Italy) rapidminer data min use cases. Bus Anal Appl 111:2

    Google Scholar 

  • Falbo C (2005) The golden ratio—a contrary viewpoint. Coll Math J 36:123–134.

    Article  Google Scholar 

  • Gao W, Iqbal J, Hu R (2021) Investigation of geomechanical characterization and size effect of soil-rock mixture: a case study. Bull Eng Geol Environ 80:6263–6274

    Article  Google Scholar 

  • Haneberg WC (2004) Simulation of 3D block populations to characterize outcrop sampling bias in bimrocks. Felsbau Rock Soil Eng J Eng Geol Geomech Tunneling 22:19–26

    Google Scholar 

  • He Z, Zhang J, Sun T (2020) Influence of maximum particle diameter on the mechanical behavior of soil-rock mixtures. Adv Civ Eng 2020:22

    Google Scholar 

  • Huang X, Yao Z, Wang W et al (2021) Stability analysis of soil-rock slope (SRS) with an improved stochastic method and physical models. Environ Earth Sci 80:1–21.

    Article  Google Scholar 

  • Irfan TY, Tang KY (1993) Effect of the coarse fractions on the shear strength of colluvium. Geotechnical Engineering Office, Civil Engineering Department

  • Jin L, Zeng Y, Xia L, Ye Y (2017) Experimental and numerical investigation of mechanical behaviors of cemented soil-rock mixture. Geotech Geol Eng 35:337–354.

    Article  Google Scholar 

  • Kalender A, Sonmez H, Medley E et al (2014) An approach to predicting the overall strengths of unwelded bimrocks and bimsoils. Eng Geol 183:65–79.

    Article  Google Scholar 

  • Khorasani E, Amini M, Hossaini MF (2019a) Effect of large blocks position on stability analysis of block-in-matrix slopes. J Min Environ.

    Article  Google Scholar 

  • Khorasani E, Amini M, Hossaini MF, Medley E (2019b) Evaluating the effects of the inclinations of rock blocks on the stability of bimrock slopes. Geomech Eng 17:279–285.

    Article  Google Scholar 

  • Khorasani E, Amini M, Hossaini MF, Medley E (2019c) Statistical analysis of bimslope stability using physical and numerical models. Eng Geol 254:13–24.

    Article  Google Scholar 

  • Khorasani E, Amini M, Hossaini SMF (2017) The Influence Assessment of Blocks Orientation on Bimslopes Stability Using Numerical Modeling. In: 4th ISRM Young Scholars Symposium on Rock Mechanics. International Society for Rock Mechanics and Rock Engineering, pp 269–272

  • Lindquist ES (1994) The strength and deformation properties of mélange. PhD dissertation. 262 pp. Dept. of Civil Engineering. Univ. of California at Berkeley. USA

  • Lv X, Zhou H (2018) Soil-rock mixture shear strength measurement based on in situ borehole pressure-shear tests. J Geophys Eng.

    Article  Google Scholar 

  • Medley EW (2001) Orderly characterization of chaotic Franciscan Melanges. Eng Geol 19:20–32

    Google Scholar 

  • Medley EW (2004) Observations on tortuous failure surfaces in Bimrocks. Felsbau Rock Soil Eng 5:35–43

    Google Scholar 

  • Medley E, Goodman RE (1994) Estimating the block volumetric proportions of melanges and similar block-in-matrix rocks (bimrocks). 1st North American Rock Mechanics Symposium. American Rock Mechanics Association, Austin, pp 851–858

    Google Scholar 

  • Medley E, Rehermann PFS (2004) Characterization of bimrocks (rock/soil mixtures) with application to slope stability problems. In: Eurock 2004 & 53rd Geomechanics Colloquium. Salzburg. Citeseer, pp 425–430

  • Medley E (1994) The engineering characterization of melanges and similar block-in-matrix rocks (bimrocks). PhD dissertation. 387 pp. Dept. of Civil Engineering. Univ. of California at Berkeley. USA

  • Medley EW (1997) Uncertainty in estimates of block volumetric proportion in melange bimrocks. In: Proceedings of the international symposium on engineering geology and the environment. Balkema, Rotterdam. pp 267–272

  • Minuto D, Morandi L (2015) Geotechnical characterization and slope stability of a relict landslide in bimsoils (Blocks in Matrix Soils) in dowtown Genoa, Italy. Engineering geology for society and territory. Springer, Berlin, pp 1083–1088

    Chapter  Google Scholar 

  • Montoya-Araque EA, Suarez-Burgoa LO, Medley EW (2020) Application of the tortuous surface method to stochastic analysis of bimslope stability. Bull Eng Geol Environ 79:5329–5340.

    Article  Google Scholar 

  • Napoli ML (2021) 3D slope stability analyses of a complex formation with a block-in-matrix fabric. International Conference of the International Association for Computer Methods and Advances in Geomechanics. Springer, Berlin, pp 744–750

    Google Scholar 

  • Napoli ML, Barbero M, Ravera E, Scavia C (2018) A stochastic approach to slope stability analysis in bimrocks. Int J Rock Mech Min Sci 101:41–49.

    Article  Google Scholar 

  • Napoli ML, Milan L, Barbero M, Scavia C (2020) Identifying uncertainty in estimates of bimrocks volumetric proportions from 2D measurements. Eng Geol 278:105831.

    Article  Google Scholar 

  • Napoli ML, Barbero M, Scavia C (2021) Effects of block shape and inclination on the stability of melange bimrocks. Bull Eng Geol Environ 80:7457–7466.

    Article  Google Scholar 

  • Napoli ML, Festa A, Barbero M (2022) Practical classification of geotechnically complex formations with block-in-matrix fabrics. Eng Geol.

    Article  Google Scholar 

  • Pan YW, Hsieh MH, Liao JJ (2008) Mechanical properties of virtual block-in-matrix colluvium. In: The 42nd US Rock Mechanics Symposium (USRMS). American Rock Mechanics Association

  • POCE (2008) Mining geotechnics and slope design studies of sungun copper mine

  • Ren M, Zhao G (2021) Prediction of compressive strength of the welded matrix-rock mixture by meso-inclusion theory. Int J Rock Mech Min Sci 139:104612

    Article  Google Scholar 

  • Riedmüller G, Brosch FJ, Klima K, Medley EW (2001) Engineering geological characterization of brittle faults and classification of fault rocks. Felsbau 19:13–19

    Google Scholar 

  • Schmüdderich C, Prada-Sarmiento LF, Wichtmann T (2021) Numerical analyses of the 2D bearing capacity of block-in-matrix soils (bimsoils) under shallow foundations. Comput Geotech 136:104232.

    Article  Google Scholar 

  • Sonmez H, Kasapoglu KE, Coskun A et al (2009) A conceptual empirical approach for the overall strength of unwelded bimrocks. ISRM Regional Symposium-EUROCK 2009. International Society for Rock Mechanics, Dubrovnik, pp 357–360

    Google Scholar 

  • Ulusay R (2013) Harmonizing engineering geology with rock engineering on stability of rock slopes. In: ISRM SINOROCK 2013

  • Vámos M, Görög P, Vásárhelyi B (2015) Landside Problem and Its Investigations in Miskolc (Hungary). In: Engineering Geology for Society and Territory-Volume 5. Springer, pp 873–877

  • Zhang Z-L, Xu W-J, Xia W, Zhang H-Y (2016) Large-scale in-situ test for mechanical characterization of soil–rock mixture used in an embankment dam. Int J Rock Mech Min Sci 86:317–322

    Article  Google Scholar 

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The research documented in this paper was performed and written by EK and MA. EM reviewed the paper in detail. Field analysis of the case study was performed by STA. MFH provided key guidelines in the research process.

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Correspondence to Emad Khorasani.

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Khorasani, E., Amini, M., Medley, E. et al. A General Solution for Estimating the Safety Factor of Bimslopes. Rock Mech Rock Eng 55, 7675–7693 (2022).

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