Proceedings, Slope Stability 2011: International Symposium on Rock Slope Stability in Open Pit Mining and Civil Engineering, Vancouver, Canada (September 18-21, 2011)

Stability Analysis of a Large Fractured Rock Slope Using a DFN-Based Mass Strength Approach

T.D. Styles AMC Consultants (UK) Ltd., Maidenhead, Berkshire, UK

J.S. Coggan Camborne School of Mines, University of Exeter, UK

R.J. Pine Camborne School of Mines, University of Exeter, UK

Abstract The global trend towards larger open pits and block cave mining is reliant on effective design at larger scales requiring improved estimates for rock mass strength. In recent years, efforts have focussed on developing synthetic Discrete Fracture Network (DFN)-based rock mass approaches. This paper provides an example of such an approach, modelling explicitly the rock fracture network within large-scale biaxial models. A conceptual large rock slope is analysed and comparisons are made with more conventional empirical strength assessments. Finally the DFN-based mass strength was modelled within a finite element solution, providing stress paths that illustrated the onset of instability during the excavation of a large slope. This example provides an insight into some of the parameters that influence the strength for a DFN-based method. In this case, fracture network geometry, strain and confinement were particularly important. The DFN-based method also demonstrated that fracture intensity has a greater influence on mass strength in low strain environments. These factors all have relevance for the determination of mass strength by any method. The Middleton Limestone was used as the basis for a conceptual case study; in this case a reduction in intact strength was necessary to allow the development of a circular slope failure mechanism. Suggestions for further research are made which are considered important if DFN-based methods are to be used for analysing the stability of large slopes.

1 Introduction The derivation of rock mass properties remains one of the most difficult tasks in rock mechanics, yet one of the most important. With the depths of modern day large open pits approaching and exceeding 1000 m, it is critical to understand and determine the significant variation from intact to overall rock mass strength. A schematic image representing this phenomenon is reproduced in Figure 1a. This shows that the strength of the rock decreases from a small and strong intact (sparsely fractured) specimen, to the relatively intensely fractured large slope.

Figure 1b demonstrates that at a bench-scale, a discontinuity-controlled mechanism can occur within a blocky rock mass. Depending on persistence, failures at bench-scale can occur predominantly over a single set of discontinuities, in which case the stability of a bench-scale failure can be largely controlled by the shear strength of a single discontinuity. At the largest scale (Figure 1c), the strength of the rock mass is more complex with both discontinuity and mass controlled failure mechanisms controlling the overall stability of the slope. Coggan et al. (1998) and subsequently Stead et al. (2006) discuss in detail the variety of methods available for simulating various scales of complex rock slope deformation.

Traditionally, the analysis of large slopes has used continuum-type circular failure (mass-controlled) methods or conventional classification-based methods, which quantify geological observations and arrive at an overall quantitative rating for the rock mass. However, conventional classification-based techniques were developed at a time when mining was at a smaller scale; like many, Stacey (2006) suggests that the basic technology for determining the rock strength aspects has changed little since the 1970s. The application of empirical approaches to the increasing scale of modern mining is being questioned, and the use of conventional continuum-based analyses is less acceptable. The influence of discontinuity-control or representation of the

Discrete Fracture Network (DFN) needs to be improved in the stability analysis of the deepening open pits. For example, the simulation of step-path failure at a large-scale has been included in recent research by several authors (Stead et al., 2004; Eberhardt et al., 2004; Yan et al. 2007; Elmo et al., 2007; Franz et al., 2007; Elmo et al., 2008; Elmo et al., 2009).

Figure 1. Effects of scale on rock strength (a), demonstrating that a potential failure mechanism is related to

the scale of study (modified after Sjberg, 1999).

1.1 The DFN-based mass strength approach An increase in both computer power and reliability of simulations is required if complex large-scale slopes are to be modelled routinely in present-day codes. Therefore the current trend for analysing strength of fractured rock masses is to mimic the behaviour of a discontinuous mass by creating a Synthetic Rock Mass (SRM). The SRM is effectively an equivalent continuum, where the discontinuous nature of a fractured mass is assessed using comprehensive numerical codes; subsequently strength properties are assigned, which represent mass behaviour at an increased scale of study (as shown in Figure 1c). To develop a realistic SRM the discontinuities within a rock mass must be mapped and a statistical model of the network created, producing a DFN. Subsequently intact rock, discontinuity strength and deformability, is included to allow comprehensive geo-mechanical modelling creating the overall behavioural model.

A specific SRM approach for slopes was first suggested by Mas Ivars et al. (2007), Read (2007) and Cundall (2008); more recent developments are detailed in Mas Ivars et al. (2011). In particular, this method uses PFC3D, (Itasca, 2011), to simulate a SRM standard suite of tests (Mas Ivars et al., 2008).

Other than Sainsbury et al. (2007), there has been minimal application of the SRM technique to rock slopes. Instead the focus has mainly been on using these techniques in underground mining, and interactions between open pit and block caving (Pierce et al., 2007; Sainsbury et al., 2008; Hadjigeorgiou et al., 2009; Deisman et al., 2010; Esmaieli et al., 2010).

An alternative approach was introduced by Pine et al. (2006) for the assessment of pillar strength, which is also reported in Elmo (2006), Flynn and Pine (2007) and Elmo and Stead (2010). The approach involves the generation of a DFN using the numerical modelling software FracMan (Golder, 2011). The DFN is then incorporated into Elfen (Rockfield Software Ltd., 2011), a hybrid finite-element method (FEM)/discrete-element method (DEM) code, which is used to derive a strength estimate for the rock mass. Specific detail on numerical routines within Elfen can be found in Owen et al. (2004) and Pine et al. (2007).

The results from a DFN-derived mass strength slope analysis are detailed within this paper; Elfen has been used to estimate the mass strength of a specific DFN (discussed in Section 2), which was previously generated by FracMan during the research by Elmo (2006). In addition, the simulation of the numerically-derived mass strength within a model of a large slope is also discussed, utilizing both limit equilibrium and finite element solutions. A summary of the approach, and ways in which mass strength has been developed and used in slope stability analysis, are presented in Figure 2. Finally, the results for shear strength determination are compared between the modelling based-approach and a more common empirical classification approach within a continuum stability analysis.

Figure 2. Sequence within the DFN-based mass strength approach, used to derive and analyse rock mass

strength in a large slope; an empirical-based method is also presented for comparison.

1.2 FEM/DEM vs. PFC approaches for biaxial/triaxial modelling As indicated above, recent efforts have focussed on developing the SRM technique, based on PFC3D modelling. FEM/DEM methods have received minimal attention, despite the recent advances in FEM/DEM approaches and alternative DEM codes (Harrison et al., 2010; Mahabadi et al., 2010, Mair and Abe, 2011). This is largely due to the limited application of FEM/DEM approaches compared with Itasca codes, which are routinely used within both mining and civil engineering.

All numerical methods have inherent limitations; in particular advanced codes such as PFC and FEM/DEM require complex input parameters and careful calibration by experienced users. The influence of constitutive relations used in FEM/DEM approaches requires further research. In comparison the ability to calibrate bonded particle models (BPM), such as PFC and PFC3D, provides a method based on micro-mechanics, subsequently no a priori assumption of a particular intact strength criterion is required, instead bond energies can be controlled to provide a unique criterion. However, past and current research has shown that BPM codes, such as PFC, have potential problems representing tensile strength (Fakhimi, 2004). Bahaaddini et al. (2011) report a lack of consistency at intermediate to high intermediate principal stresses, in their comparisons between PFC3D and a published account of physical modelling. In addition, Mas Ivars et al. (2011) also state that elevated tensile strength is an issue within the current SRM approach.

Subsequently, attention is required to develop both BPM and FEM/DEM approaches. In addition there should be a focus on comparing biaxial/triaxial data from different 2-D and 3-D numerical codes, constraining them against fully characterised field cases (Styles et al., 2010).

2 Case study material Modified Hoptonwood Limestone The first step of the numerical approach used in this paper, shown in Figure 2, is the characterisation of the DFN within the rock mass. Rogers et al. (2010) provides detail on the benefits of a mine-scale DFN approach and the different techniques available, with a view to developing more detailed SRM models. In this case the Hoptonwood Limestone mapped within Middleton Mine in Derbyshire, provided a basis for a suitable case study considering the previous mapping and FracMan modelling conducted by Elmo (2006). Although the mine is an underground operation, the in-situ mapping of the rock mass provided data suitable for modelling of both underground excavations (as per Elmo, 2006; Pine et al., 2006; Flynn and Pine, 2007; Elmo and Stead 2010) and slopes. The Hoptonwood Limestone is dominated by mostly vertical to sub-vertical jointing with sparse (widely spaced) bedding.

In the example large scale slope which follows, a material is used that consists of jointing similar to the Hoptonwood Limestone. As shown in Figure 3 the relative orientation of the overall slip surface changes from approximately sub-parallel for much of the jointing in the upper zone, to approximately sub-normal to much of the jointing in the toe zone. To allow for this in the slope stability analysis the shear strengths derived for the rock mass using the Elfen models were varied by rotating the applied stresses relative to the joint orientations (see Figure 4). This resulted in relatively low shear strengths in the upper zone (e.g. model RE) and slightly higher shear strengths in the toe zone (horizontal model). During this research, a fixed width to height ratio was used, with models 2.8 m wide and 7 m in height, reflecting typical width to height ratios used for uniaxial compressive strength tests. As discussed in Section 5, recommendations for future work include further analysis of the representative elementary volume for the rock mass, and associated modelling of the effects of confining stress and varying width to height ratio on the modelled discrete fracture network for different stress environments.

It was found that using the UCS and related strengths for the Hoptonwood Limestone directly, provided a slope that was too strong to fail in any significant way. Consequently the intact properties were downgraded to provide a suitable material for examining failure in the slope modelling, as detailed in the following section.

Figure 3. Arbitrary fracture network within a large slope showing that with dominant sub-vertical fractures,

shear strength can be greater within the toe of slope where shear is against the dominant fracture orientation.

Figure 4. Sections taken through Middleton DFN to create biaxial models for Elfen modelling.

3 Numerical approach

3.1 Derivation of rock mass strength Large scale 2-D biaxial tests on fractured rock can be simulated using a comprehensive numerical method, such as Elfen (Rockfield Software Ltd., 2011). The aim of such tests is to derive a compressive strength for the rock mass; consequently multiple biaxial tests are used to generate a strength envelope for an equivalent continuum, which represents the discontinuous nature of the rock mass.

As described in Section 2, a reduction of intact strength was necessary; this provided gave properties for a new rock mass which retained the original DFN, created for Middleton Mine by Elmo (2006). The Mohr-Coulomb and Rotating Crack intact strength properties of the Hoptonwood Limestone were quartered, to provide the intact strength parameters, as listed in Table 1. The properties listed and additional numerical parameters, including damping coefficients, penalties (which are equivalent to stiffness), loading rate and mesh size remain the same as reported in Elmo (2006), as based on a calibration study.

Table 1. Strength parameters for the Hoptonwood Limestone, and the properties of the downgraded rock material (with the Middleton DFN), which was used in the Elfen biaxial models.

Parameter

Strength values for biaxial models: Hoptonwood Limestone* Downgraded

Intact-material

properties

Mohr-Coulomb + Rotating

Crack

Cohesion 9 MPa 2.3 MPa Friction Angle 40 11.8 Dilation Angle 5 5 Tensile Strength 3.8 MPa 1 MPa Fracture Energy 19.5 J/m2 4.9 J/m2

Discontinuity properties

Friction 30 Cohesion 100 kPa Normal penalty 1 GPa/m Tangential penalty 0.2 GPa/m

*The derivation of the intact strength parameters for the Hoptonwood Limestone is detailed in Elmo and Stead (2010); discontinuity properties were obtained from Pine et al. (2006) and remain the same for both the original and downgraded material.

During the biaxial simulations within Elfen, the detection of the actual peak and yielding behaviour of models was difficult, especially at high confinements, where clear fracture planes did not develop. The choice of peak strength appears to be strain-related; an example of this is given in Figure 5. The peak that occurs at the lower axial strain indicates the onset of failure, whereas by choosing values from peaks that occur up to 3% axial strain, it is assumed that the final actual peak in the maximum principal stress (1max) is exposed.

Figure 5. Stress-strain data from biaxial tests on RE section, demonstrating that two sets of peak strengths can

be inferred from each of the confined models.

Elmo and Stead (2010) investigate the influence of DFN variation with respect to pillar strength. A similar aspect was explored during this research, although with emphasis on rock mass strength. Accordingly an additional section (RC) was modelled based on a different fracture network representation of the rock mass from Elmo (2006); as shown in Figure 6 both sections RC and RE have similar fracture intensities. The modelling results are summarised in Figure 7. These show that there can be significant variations in biaxial strength for the different joint patterns at the same joint intensity, particularly at low confining pressures. This is clearly of significance for the determination of both numerical and empirical strength envelopes.

It was also found that the rock mass strength taken from lower axial strain is subject to a larger variation, having a lower coefficient of determination (R2) than when the strength is taken from higher axial strain, as illustrated in Figure 7. This signifies the importance of strain magnitude relative to the failure environment; with a greater influence of DFN variation in low strain surroundings.

Figure 6. Comparison of two sections (RC and RE), with similar fracture intensities.

Figure 7. Comparison of strength data from different axial strains within two sections (RC and RE), which

have similar fracture intensities, with non downgraded/original properties.

Confinement (3) also has a significant influence on the model behaviour, with large differences between the low strength unconfined models, and the very strong highly confined simulations. In general all models were run with 0, 0.5, 1 and 2MPa 3, although to increase the understanding of mass strength at high 3, a single simulation was completed using the RE section with a higher 3 of 4 MPa, as shown in Figure 8. The results including the 4 MPa simulation suggest a linear 1 / 3 response. Subsequently in this case, the Mohr-Coulomb criterion was assumed to be a more appropriate strength criterion than a non-linear approach such as Hoek-Brown, which gave a significantly lower strength at high confinement.

3.2 Simulation of the equivalent continuum 3.2.1 Limit state modelling

A zoned model, shown in Figure 9, was created to analyse the influence of the changing shear strength along circular failure plane. As shown in Table 2, a limit equilibrium analysis using Slide (Rocscience, 2011), showed a zoned 55 angle and 1000m high slope to have a FOS of on average 1.6, depending on the Mohr-Coulomb strength used from Elfen testing. In addition a homogeneous un-zoned model was also analysed, with a strength based entirely on the weak orientation model. The FOS of this was slightly lower, at on average 1.5.

Figure 8. Data from biaxial tests on downgraded RE section, which can be used to derive a Mohr-Coulomb

mass strength.

Table 2. Results from an analysis of a numerically-derived strength for an equivalent continuum making up a 55 1000 m slope.

Model Composition Variables controlling Mohr-

Coulomb strength: Mohr-Coulomb strength from

Elfen testing FOS from Slide Axial strain Confinement (MPa) Cohesion (MPa) Friction ()

Zoned Top 2/3 RE

Up to 1.5% 0, 0.5, 1 and 2 0.771 48

1.5 Bottom 1/3 Horizontal 0.813 62

Zoned Top 2/3 RE

Up to 3% 0, 0.5, 1 and 2 0.876 53

1.6 Bottom 1/3 Horizontal 1.08 64

Zoned Top 2/3 RE

Up to 3% 0, 1 and 2 0.577 54

1.7 Bottom 1/3 Horizontal 0.546 66

Homogeneous 100% RE Up to 1.5% 0, 0.5, 1 and 2 0.771 48 1.4 Homogeneous 100% RE Up to 3% 0, 0.5, 1 and 2 0.876 53 1.6 Homogeneous 100% RE Up to 3% 0, 1 and 2 0.577 54 1.5

Figure 9. Rotation of biaxial stresses with depth to allow the analysis of changing shear strength with depth,

demonstrating how large-scale Elfen biaxial models can be used to derive slope mass strength.

The Mohr-Coulomb strength derived from Elfen testing was also used with the Hoek and Bray circular failure charts (Hoek and Bray, 1981). In comparison with Slide, the Hoek and Bray charts returned a FOS that was slightly (10%) lower for the homogeneous slope model. Further analysis using the failure charts demonstrated the limited sensitivity to cohesive strength for a slope at this scale.

3.2.2 Finite element modelling

Finite element modelling was undertaken using Phase2 (Rocscience, 2011), with excavation of the slope in stages, as shown in Figure 10. The weakest slope material was chosen, composed entirely of the mass strength from the RE model, for a back-analysis. The shear strength reduction (SSR) module within Phase2 was used, which enables the determination of Mohr-Coulomb failure parameters which apply at a FOS of 1. This showed that the critical stress reduction factor (SRF) was 1.31, subsequently new mass strength properties were calculated and checked within Slide, giving a factor of safety of 1.1, as shown in Table 3. Note that in this case it was assumed there was no tectonic stress; with K-ratio related instead relating to the Poissons ratio providing a value of 0.3 in and out-of plane. As discussed by Stacey et al. (2003), an increase in K-ratio and slope height can result in increased strain. The specific influence of effects of K-ratio on the estimated FOS is to be analysed as part of further work.

Table 3. Results from a SSR Phase2 simulation on a 55 1000 m high slope; with resulting SRF and consequent mass properties, which were then checked in a Slide model.

Phase2 Mass Strength Inputs: Critical

SRF

Resulting Mass strength from SSR for FOS = 1 FOS from Slide (of a Slope with mass strength from

critical SRF) Cohesion (kPa) Friction ()

Cohesion (kPa) Friction ()

577 54 1.31 440 46 1.1

The stress within and near the failing zone in the base of the large slope was investigated using Phase2 with stress path diagrams for Points A, B and C shown in Figure 10. This analysis showed that only at Point C was failure expressed; as illustrated in Figure 11 the stress-path plots show incipient failure during the transition between stages 4 to 5 (excavation of the last 600-800 m of the slope). Also failure can be tracked by the stress tensors, which rotate during failure, as illustrated in Figure 12.

Figure 10. Phase2 model of 55 large slope. The excavation sequence use is illustrated, along with the stress

monitoring points that were chosen.

Figure 11. (a) Mohr-Coulomb plot of stress within Point C in base of a Phase2 model at Point C (using data

from Table 3); (b) p-q stress path derived from the Mohr-Coulomb plot.

Figure 12. Phase2 model of 55 1000m slope. Scaled stress tensors are included to indicate the change in the

principal stress during failure (mesh density illustrated in Figure. 10).

4 An empirical approach One of the most frequently used methods to derive rock mass strength, is to use the combination of the empirical classification system, GSI (Hoek et al., 1995) feeding into the program RocLab (Rocsciemce, 2011), providing both Hoek and Brown and Mohr-Coulomb mass strength criterion. GSI, mi and UCS values, can be input straight into Slide, which includes the RocLab calculation, for comparison against the numerically derived strength for the conceptual large rock slope. The UCS chosen was 12 MPa, based on a quarter of the compressive strength of the Hoptonwood Limestone suggested by Pine et al. (2006), per Table 1 and downgraded to consider slope failure, as described in Section 2.

A range of values have been suggested for the GSI of the Hoptonwood Limestone; Pine et al. (2006) listed a typical GSI of between 60 and 70, whereas Elmo (2006) matched data from Elfen testing of pillars to between 40 and 80. The upper end of this range was considered within RocLab, and directly entered into Slide, providing the results presented in Table 4. Two mi values, 10 and 15 were used; the mi suggested by Pine et al. (2006) is 10 whereas the guidance for limestone within RocLab is 12 3.

Table 4. Rock mass strength for the downgraded Hoptonwood Limestone, derived from the Generalised Hoek-Brown Criterion, and inputted directly into Slide to give a range of FOS.

GSI mi UCS (MPa) Resulting FOS from Slide 60 10 12 0.9 60 15 12 1.0 80 10 12 1.2 80 15 12 1.3

The FOS, derived from the coupled Hoek-Brown-GSI approach, is comparable if somewhat lower than the FOS suggested by the numerical DFN-based method. As with the numerical method, a range of FOS has been given. This demonstrated that the strength from the Hoek-Brown-GSI approach is dependent on the GSI and mi, which is perhaps more difficult to relate quantitatively to a failure environment than the strain and confinement dependencies within the DFN-based technique.

5 Conclusions The derivation of a conceptual DFN-based model for mass strength in a slope context, has illustrated that there are a number of factors that can have a significant influence on the derived strength, such as fracture orientation, confinement and the degree of strain at which rock mass strength is taken. During the modelling undertaken it was assumed that a confinement of up to 2 MPa and axial strains of up to 3% were representative of the slope-related failure environment.

Analyses showed that the variation in the mass strength between different fracture orientations has a greater influence on the DFN-based mass strength in low strain environments. In this case it is suggested that for a more reliable mass strength, many simulations should be completed for different fracture patterns (all with a similar fracture intensity), and variation of the width to height ratio should be considered (Elmo and Stead, 2010). It must also be noted that due to computation limits, this work has used two-dimensional models to estimate rock mass strength. In order to simulate fracture extension within a fracture network in three-dimensions (3D), the Elfen code requires further development for a parallel processing platform.

Limit equilibrium modelling of the DFN-derived mass strength showed that, in this example the dominant fracture orientation relative to the direction of maximum principal stress had little significance. Results from FEM simulations were presented, demonstrating the potential of using stress paths to detect instability during the excavation of a large slope.

Comparisons were made between the numerical DFN-mass strength approach and an empirical method, on the same downgraded material, showing that strengths derived from the DFN approach are up to 40% greater than those derived through an empirical approach. This demonstrated the important influences of fracture orientation and strain, which cannot be considered directly within empirical approaches. However, it should be noted that when analysing a DFN with many joints, such as that collected from Middleton Mine, the Hoek-Brown criterion should be used with caution.

To develop a numerical approach with more confidence there needs to be a more detailed back analysis of the behaviour of mixed structural and mass-controlled slope failures. Further biaxial modelling, and ultimately triaxial modelling, is also necessary over a variety of scales to fully characterise a rock mass; on the smallest scale the intact strength of the rock-bridges needs to be established, whereas on the large scale the representative elementary volume needs to be considered.

Elmo and Stead (2010) report that slender pillars have a highly variable stress-strain response; this behaviour is confirmed for biaxial models used in this research. Only a limited number of DFN realisations were used in the current modelling. Ideally this needs to be extended to capture the full range of the likely strength envelope. This requires improved efficiencies in both coding and computer speeds for more routine use. More importantly there needs to be significant advances in the characterisation of a fractured rock mass, to provide a reliable foundation for a DFN-based approach such as that which is discussed in this paper.

6 Acknowledgements Funding for research was part of a UK Engineering and Physical Sciences Research Council project (EPSRC, Grant No. EP/C518713/1). Additional support and collaboration was provided by Rockfield Software Ltd. as part of an associated grant (EP/C518721/1).

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