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A General Solution for Estimating the Safety Factor of Bimslopes

DOI:10.1007/s00603-022-03050-z
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Emad Khorasani
Emad Khorasani
Emad Khorasani
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Mehdi Amini
Mehdi Amini
Mehdi Amini
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Edmund Medley at Dr. Edmund Medley, PE, PG CEG, D.GE, F. ASCE
Edmund Medley
Sadegh Tarigh Azali at Rahsaz Tarh Consulting Engineers Company (مهندسین مشاور رهسازطرح)
Sadegh Tarigh Azali
  • Rahsaz Tarh Consulting Engineers Company (مهندسین مشاور رهسازطرح)
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Abstract and Figures

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.
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Vol.:(0123456789)
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Rock Mechanics and Rock Engineering (2022) 55:7675–7693
https://doi.org/10.1007/s00603-022-03050-z
ORIGINAL PAPER
A General Solution forEstimating theSafety Factor ofBimslopes
EmadKhorasani1 · MehdiAmini2· EdmundMedley3· SadeghTarighAzali4· MohammadFarouqHossaini5
Received: 20 May 2022 / Accepted: 24 August 2022 / Published online: 13 September 2022
© The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2022
Abstract
Bimslopes are slopes underlain by block-in-matrix rocks/soils (bimrocks/bimsoils), which are heterogeneous geomateri-
als 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.
Highlights
• 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.
Keywords Bimrocks· Bimslopes· Slope stability· Numerical modeling· Sensitivity analysis
* Emad Khorasani
emad.khorasani@ut.ac.ir
Mehdi Amini
mamini@thurber.ca
Edmund Medley
emedley@bimrocks.com
Sadegh Tarigh Azali
sadeghazali@gmail.com
Mohammad Farouq Hossaini
s.hossaini@unsw.edu.au
1 School ofMining Engineering, College ofEngineering,
University ofTehran, Northern Kargar Street, Tehran, Iran
2 Thurber Engineering Ltd., Vancouver, Canada
3 Terraphase Engineering, Oakland, CA94612, USA
4 RahsazTarh Consulting Engineers, Tehran, Iran
5 School ofMinerals andEnergy Resources Engineering,
UNSW, Sydney, Australia
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... Under the rainfall conditions, an erosion failure was observed in the soil-rock mixture slope, and the increasing rock content would densify the soil skeletons, decrease the migration of fine particles, and finally weaken the erosion effect [39]. The groundwater level also has influences on the stability of bimslopes, i.e., the normalized safety factor was recommended to reduce by 25% when the bimslopes was fully saturated [40]. Large-deformation failure mechanisms of soil-rock mixture slopes were analyzed by Zhao et al. [41]. ...
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A wide range of heterogeneous geological units composed of strong rock blocks enclosed in a bonded matrix of fine texture exists worldwide. Such geomaterials belong to geotechnically complex formations and are often referred to as bimrocks (block-in-matrix rocks) or bimsoils (block-in-matrix soils), as a function of their matrix characteristics and the interface strength between the matrix and blocks. Stability problems occurring in such complex geomaterials have been analysed almost exclusively by means of deterministic approaches and with the aim of investigating the effects of variable block contents on their mechanical behaviour. However, bimrocks and bimsoils can present very different internal block-in-matrix arrangements and properties according to their forming process and, consequently, significantly dissimilar mechanical behaviours. Therefore, the aim of this paper was to statistically investigate and compare the stability of theoretical slopes in the most widespread bimrock formations, i.e. sedimentary and tectonic melanges. These formations are characterised by substantial differences in their rock inclusion geometry. To this aim, a great number of 2D slope models were generated to enclose blocks with variable shapes, dimensions, arrangements, inclinations and contents. To obtain statistically based results, fifteen configurations were analysed for each block content and geometrical configuration considered. The results obtained indicate that block shapes and orientations significantly affect the stability of slopes in bimrocks only when the block contents are greater than 40%. Moreover, it is demonstrated that blocks inclined 0° to the horizontal provide the most tortuous and irregular failure surfaces and, consequently, the highest safety factors.
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With the steady development of the development of the western region in China, the construction of mountain highways has developed rapidly, and the soil-rock mixed filler, as an excellent filler, is widely used in the subgrade filling of mountain highways. Unlike ordinary fine-grained soil, the source of the soil-rock mixtures (S-RMs) is not unique, and the particle size difference is large and the water content is not uniform, resulting in very complicated mechanical properties. But the current highway embankment codes are still mainly established on the fine-grained soil. It is not fully applicable to soil-rock filled embankment. Based on soil-rock filled embankment engineering practice, this research uses a large-scale direct shear test to research the mechanical characteristics of the S-RMs with different maximum particle diameters. According to the large-scale direct shear test of S-RMs with different maximum particle diameters, the shear displacement vs shear stress curve, shear dilation, and strength characteristics with maximum particle diameter were analyzed. Results demonstrate that whether secondary hardening occurs mainly depends on the normal stress and the maximum particle diameter of the filler. At different maximum particle diameters, the horizontal displacement vs vertical displacement curves of the S-RMs can be roughly divided into continuous shearing and beginning of shearing and quick dilation. And the shear strength increases with the increase of the maximum particle diameter. Moreover, the cohesion decreases first and then increases with the increase of the maximum particle diameter, and the internal friction angle increases with the increase of the maximum particle diameter. Therefore, some RBs with large particle diameter added to filler can effectively improve the shear strength of the S-RMs, which may be valuable for realistic engineering.
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The terms “bimrocks”, “bimsoils” and “soil-rock mixtures” indicate different and very common types of geological units with a block-in-matrix fabric that are also “geotechnically complex formations” and are characterized by an internal heterogeneity, and spatial variability of mechanical parameters and lithological compositions. Due to this internal complexity, the understanding of their geomechanical behavior presents a key challenge in geotechnical engineering. However, the lack of a standardized and clear terminology complicates the discrimination of different types of complex formations and their internal mechanical properties, which leads to inconsistency in the literature and research studies. This inconsistency causes misunderstandings, with possible practical implications for the characterization, analysis, design and construction of engineering works. By a combination of geological and geotechnical observations, we propose a new classification for geotechnically complex formations, with particular attention to those with a block-in-matrix internal fabric. Four properties are at the base of this new classification and have a primary role in controlling the geotechnical behavior of block-in-matrix units (bimunits): (i) the composition (i.e., lithology, degree of lithification/consolidation, nature, and rheology) of blocks and the matrix that affects the water sensitivity, (ii) the degree of internal anisotropy (DA) of the block-in-matrix fabric, (iii) the degree of stratal disruption and mixing, and (iv) the volumetric block proportion (VPB). As a result, we classified bimunits in those with “anisotropic”, “isotropic”, and “mixed” (i.e., different behavior depending on the DA of the matrix) textures and, each of these types, into block-in-matrix rocks and block-in-matrix soils (bimrocks and bimsoils in the following). According to the water sensitivity of the matrix, bimrocks are also differentiated into “hard” and “soft”. The novelty of the classification is that it is not limited to few types of geotechnically complex formations (e.g., flysch) but it can be easily applied to all field-based investigations of the different types of complex formations, regardless of their internal degree of stratal disruption, composition, and mechanical response to water sensitivity.
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Soil-rock mixture (S-RM) exerts a major control on slope stability. Baidian County in southeastern China was selected as a case study to better understand the effect of S-RM on potential slopes. The developed slope deposits in Baidian County mainly consist of different fractions of soil and fragmented rocks with random structure and poor sorting, which is characteristic of a typical S-RM. A series of large in situ horizontal push-shear tests was conducted on selected sites under natural conditions to investigate the mechanical strength characteristics and size effect of the regional S-RM. The results show a larger internal friction angle and smaller cohesion value than reported in previous experimental studies, which directly correspond to block proportion by weight (WBP) of S-RM. The mechanical parameters of the various S-RM sizes exhibit two distinct trends that follow exponential regression functions. The size effect is assumed to be influenced by the non-uniform coefficient (Cu). These results provide important insight on the engineering properties of S-RM and guidance for the design of suitable slope mitigation strategies.
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As a special and widely distributed geological material, the matrix-rock mixture (block-in-matrix texture) has been worldwide focused on its complex physical and mechanical properties for 25 years. However, the macro-meso mechanical relationship of matrix-rock mixture has not been well clarified so far, leading to the unclear understanding of its mechanical behavior. In this paper, the welded matrix-rock mixture is considered as a two-phase composite material, and a mesoscopic mechanical method is presented for calculating the uniaxial compressive strength (UCS). The influence of volumetric block proportion of rock (VBP) and mechanical contrast of meso components (i.e. UCS ratio (SR) and modulus ratio (MR) of rock to matrix) on the strength and the failure mechanism of the matrix-rock mixture is illustrated by the meso-inclusion theory. To avoid the rock damage in the welded mixture, it is suggested that the SR of rock to matrix should be larger than 1.5 for the low stiffness ratio of rock to matrix (e.g. MR ≤ 5), while for the mixture with high stiffness contrast (e.g. 5 < MR < 100) the SR of rock to matrix should be larger than 2. For the common case of strong rock-weak matrix mixture, the reinforced effect of VBP is positive with the MR of rock to matrix but seems to be insignificant when MR > 100. Meanwhile, the Weibull function is adopted to describe the strength property of the matrix in view of its strength randomness contributing to the matrix-rock mixture. It is shown that the strength evolution of the mixtures can be effectively predicted by the present model considering the Weibull distributed strength of the matrix, based on the comparison with the published experimental data and the discussion of existed empirical formulas.
3D Slope Stability Analyses of a Complex Formation with a Block-in-Matrix Fabric
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  • Jan 2021
Heterogeneous rock bodies composed of strong rock blocks surrounded by a weaker finer-grained matrix are often referred to as “BIMrocks” (Block-In-Matrix rocks). These complex formations present a high spatial, dimensional and lithological variability, which makes their characterization an extremely challenging task. As a consequence, geopracticioners have often planned engineering works in bimrocks ignoring the presence of the stronger rock inclusions. However, it is essential that blocks be considered in the analyses in order to obtain reliable results. In fact, rock inclusions strongly affects the strength, deformability and failure surfaces of these geomaterials.
Identifying uncertainty in estimates of bimrocks volumetric proportions from 2D measurements
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Chaotic geological bodies composed of rock inclusions of different lithology and size enclosed in a weaker matrix are often referred to as bimrocks (block-in-matrix rocks). When dealing with these challenging and widespread geomaterials, a major concern for geopractitioners is the estimation of block content, which has been demonstrated to strongly affect the overall mechanical behaviour of bimrocks. Since the estimation of this parameter is not a simple matter, stereological principles are generally applied to infer 3D block contents from 1D or 2D measurements. However, they are often fraught with a high magnitude of error. In this study, a statistical approach was developed to determine the uncertainties associated with estimates of the 3D block proportions from 2D measurements. A Matlab code was implemented to generate heterogeneous models with a size distribution typical of bimrocks. An uncertainty factor is provided related to the size of the outcrop area investigated and the 2D block content to adjust the initial 2D estimates. It was found that a larger investigation area increases the reliability of the 2D measurements and as actual volumetric block proportion increases, the uncertainty decreases. The results obtained through this procedure were subsequently compared with previous findings from the literature concerning the uncertainty in estimates of the VBP from 1D measurements. The outcome of this comparison highlights the strength of the procedure described in this paper.
Application of the tortuous surface method to stochastic analysis of bimslope stability
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  • Jul 2020
This article presents a summary of the research on the novel tortuous surface method to stochastically analyze the stability of two-dimensional bimslopes, which are slopes composed of bimrocks or bimsoils. Tortuous failure surfaces (TFSs) are slip surfaces that develop around blocks when bimslopes fail. The method was automated through an algorithm that locates a slip surface passing around the blocks as if it were the solution of a “maze puzzle.” Slope stability analyses were performed using the limit equilibrium method (LEM). To compare many different models, the normalized factor of safety of a TFS (\(f_{\mathrm {n}}^{\ast }\)) was computed. \(f_{\mathrm {n}}^{\ast }\) is obtained by dividing the fs from the TFS by the fs from the surface potentially produced when there are no blocks (the critical circular surface or the matrix-only surface (MOS)). Two groups of analyses were performed. First, two tortuosity parameters, the tortuous length ratio (TLR) and the average tortuous width (ATW), were analyzed through the evaluation of a hypothetical slope of 10 m height and 35∘ inclination with varying block proportions. Second, similar hypothetical models were developed with three different values of the slope height, slope inclination, and ratio of the unit weight of the blocks to the unit weight of the matrix; then, the behavior of \(f_{\mathrm {n}}^{\ast }\) for different values of both the cohesion and friction angle of the matrix was presented in a sensitivity analysis. A prime conclusion of the research is that for prudent geotechnical design, stochastically based stability analyses of bimslopes are far preferable to deterministic analyses.